Class 10th Mathematics AP Board Solution
Exercise 14.1- A survey was conducted by a group of students as a part of their environment…
- Consider the following distribution of daily wages of 50 workers of a factory.…
- The following distribution shows the daily pocket allowance of children of a…
- Thirty women were examined in a hospital by a doctor and their of heart beats…
- In a retail market, fruit vendors were selling oranges kept in packing basket.…
- The table below shows the daily expenditure on food of 25 households in a…
- To find out the concentration of so_2 in the air (in parts per million, i.e.,…
- A class teacher has the following attendance record of 40 students of a class…
- The following table gives the literacy rate (in percentage) of 35 cities. Find…
Exercise 14.2- The following table shows the ages of the patients admitted in a hospital…
- The following data gives the information on the observed life times (in hours)…
- The following data gives the distribution of total monthly household…
- The following distribution gives the state-wise, teacher-student ratio in…
- The given distribution shows the number of runs scored by some top batsmen of…
- A student noted the number of cars passing through a spot on a road for 100…
Exercise 14.3- The following frequency distribution gives the monthly consumption of…
- If the median of 60 observations, given below is 28.5, find the values of x and…
- A life insurance agent found the following data about distribution of ages of…
- The lengths of 40 leaves of a plant are measured correct to the nearest…
- The following table gives the distribution of the life-time of 400 neon lamps…
- 100 sumames were randomly picked up from a local telephone directory and the…
- The distribution below gives the weights of 30 students of a class. Find the…
Exercise 14.4
- A survey was conducted by a group of students as a part of their environment…
- Consider the following distribution of daily wages of 50 workers of a factory.…
- The following distribution shows the daily pocket allowance of children of a…
- Thirty women were examined in a hospital by a doctor and their of heart beats…
- In a retail market, fruit vendors were selling oranges kept in packing basket.…
- The table below shows the daily expenditure on food of 25 households in a…
- To find out the concentration of so_2 in the air (in parts per million, i.e.,…
- A class teacher has the following attendance record of 40 students of a class…
- The following table gives the literacy rate (in percentage) of 35 cities. Find…
- The following table shows the ages of the patients admitted in a hospital…
- The following data gives the information on the observed life times (in hours)…
- The following data gives the distribution of total monthly household…
- The following distribution gives the state-wise, teacher-student ratio in…
- The given distribution shows the number of runs scored by some top batsmen of…
- A student noted the number of cars passing through a spot on a road for 100…
- The following frequency distribution gives the monthly consumption of…
- If the median of 60 observations, given below is 28.5, find the values of x and…
- A life insurance agent found the following data about distribution of ages of…
- The lengths of 40 leaves of a plant are measured correct to the nearest…
- The following table gives the distribution of the life-time of 400 neon lamps…
- 100 sumames were randomly picked up from a local telephone directory and the…
- The distribution below gives the weights of 30 students of a class. Find the…
Exercise 14.1
Question 1.A survey was conducted by a group of students as a part of their environment awareness programmed, in which they collected the following data regarding the number of plants in 20 houses in a locality. Find the mean number of plants per house.
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)
Answer:Let’s find mean of the data using direct method.
First, construct a table for ease of calculation.
![](data:image/png;base64,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)
Mean is given by
![](data:image/png;base64,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)
⇒ Mean = 162/20
⇒ Mean = 8.1
Thus, mean number of plants per house is 8.1.
Question 2.Consider the following distribution of daily wages of 50 workers of a factory.
![](data:image/png;base64,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)
Find the mean daily wages of the workers of the factory by using an appropriate method.
Answer:Let’s find mean of the data using assumed mean method.
We are using assumed mean method to avoid miscalculation and false answer, as xi’s are large in this question.
First, construct a table for ease of calculation.
![](data:image/png;base64,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)
Mean is given by
![](data:image/png;base64,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)
Where A = assumed mean
⇒ ![](data:image/png;base64,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)
⇒ Mean = 325 – 12 = 313
Thus, mean daily wages of the workers is Rs. 313.
Question 3.The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is ` 18. Find the missing frequency f.
![](data:image/png;base64,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)
Answer:To find f, we’ll need to find mean pocket allowance by direct method and equate it to the given mean pocket allowance, 18.
So, let’s construct a table finding midpoints and stating frequencies.
![](data:image/png;base64,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)
Mean is given by
![](data:image/png;base64,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)
⇒
[given, mean = 18]
⇒ 18(44 + f) = 752 + 20f
⇒ 792 + 18f = 752 + 20f
⇒ 20f – 18f = 792 – 752
⇒ 2f = 40
⇒ f = 40/2
⇒ f = 20
Thus, the missing frequency f is 20.
Question 4.Thirty women were examined in a hospital by a doctor and their of heart beats per minute were recorded and summarized as shown. Find the mean heart beats per minute for these women, choosing a suitable method.
![](data:image/png;base64,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)
Answer:We shall use assumed mean method to find mean heart beats per minute, as this data has large values of xi’s and has a risk of miscalculation. But by using assumed mean method, we’ll be able to solve it with ease and more accuracy.
![](data:image/png;base64,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)
Mean is given by
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ Mean = 75.9
Thus, mean heart beats per minute of these women is 75.9.
Question 5.In a retail market, fruit vendors were selling oranges kept in packing basket. These baskets contained varying number of oranges. The following was distribution of oranges.
![](data:image/png;base64,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)
Find the mean number of oranges kept in each basket. Which method of finding the mean did you choose?
Answer:We shall use assumed mean method to find mean number of oranges.
So, while converting data into exclusive type won’t change any calculation in finding mean, we are however converting the inclusive data type to exclusive data type for better representation.
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)
Mean is given by
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIgAAAAtCAMAAABCtdM9AAAAAXNSR0IArs4c6QAAAJNQTFRFAAAAAAAAAAA6AABmADqQAGZmAGa2OgAAOgBmOjoAOjpmOjqQOmY6Oma2OpDbZgAAZgA6ZgBmZjoAZjo6ZmY6ZpCQZpC2ZpDbZra2ZrbbZrb/kDoAkGYAkGY6kLbbkNu2kNv/tmYAtmY6tv/btv//25A625Bm27Zm27aQ29uQ2/+22////7Zm/9uQ/9u2//+2///byW8DugAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACwElEQVRYR+1X23abMBCUSGp6i+0mbtOUtjFpSNMYjP7/6zqrG4LIgDiy+lI92Oggdkezo10tY/9HcgYqbscazsUPzulfjprzb8kAiUI5EyUBEMWKVRYIkKQDwpr84pGQtBsAaPKe58H0zOxUfCU9lAAyoCAtEBMcEkUOwWhOmmvOP/YJOjMjoEEFR8rThKbJ75j4nlIjFBQdHBdIeXl4FalzMwKdmp1bRqR0h9o9OxBWZXsnNBXIcIDQNNFQXq1G/h2QUp1fV6yU2ZJrpLKHRp6amlMsquwnO97YaYrYOFkLxQWupSjEA8+u/uRmmgCICgJGZQI0UGcqsZrAHDdjQHDC9RFHue6qYiBRojh9Aikaehj7XkaARBrB/2IckJ/JE2oHorA1FoVmCKTJodNu6Gm73Ukj9Zvr5UDKz3nvYwfIbG7b7T1lG1F8VUkHNTG7pU39fsf5lbpEPeX0dHq0n371Y7MMyL7EMa8vX3Tyv2PPqM2Q+kGUxFWTv9+zarRK4jg4qaIfmgBG9pRkyrVKw1QT7XmTCUD/aOpLG/BOFbT//g1nISNw3Lx9lEA6NDJMFkhXLDw7bD444FHyzVBQO62OPcH1FsRf7NYKA51mDMRKPN/gNmUYGQWi7uldGu+dmpDQYOcA7zAio7w6+BjxhIa2MihfC0MDZSDnSSBWHrXS6RxGap2HbIVdyMhG5x7Ffs1xk3y6BYY1O+4IiLxT0fTE0NjbjRObBYzYFE8P5Aw5I/uCVPuALPKCG15DSjEvPVjolbxwuSrxARnr+GYLKcbC0Y4vhoPZNsY6vtlGoiwc6fii2J9t5ETHN/v7eAu9HV888wGWfB1fwOfxlno6vnjGgyy97viCPo+22NPxRbMdZMjT8QV9H2uxt+OLZTzAjr/jCzAQaelkxxfJz6SZyY5v0kKcBdMdXxw/U1YmOr6/Oz5IPNkwk4IAAAAASUVORK5CYII=)
⇒ ![](data:image/png;base64,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)
⇒ Mean = 22 + 0.3125
⇒ Mean = 22.3125
Thus, mean number of oranges is 22.31.
We have used assumed mean method here, because of larger data values of fi’s. Assumed mean method gives result to accuracy and ease when data is large.
Question 6.The table below shows the daily expenditure on food of 25 households in a locality.
![](data:image/png;base64,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)
Find the mean daily expenditure on food by a suitable method.
Answer:Let’s find mean of the data using assumed mean method for ease of calculation.
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)
Mean is given by
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIgAAAAtCAMAAABCtdM9AAAAAXNSR0IArs4c6QAAAJNQTFRFAAAAAAAAAAA6AABmADqQAGZmAGa2OgAAOgBmOjoAOjpmOjqQOmY6Oma2OpDbZgAAZgA6ZgBmZjoAZjo6ZmY6ZpCQZpC2ZpDbZra2ZrbbZrb/kDoAkGYAkGY6kLbbkNu2kNv/tmYAtmY6tv/btv//25A625Bm27Zm27aQ29uQ2/+22////7Zm/9uQ/9u2//+2///byW8DugAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACwElEQVRYR+1X23abMBCUSGp6i+0mbtOUtjFpSNMYjP7/6zqrG4LIgDiy+lI92Oggdkezo10tY/9HcgYqbscazsUPzulfjprzb8kAiUI5EyUBEMWKVRYIkKQDwpr84pGQtBsAaPKe58H0zOxUfCU9lAAyoCAtEBMcEkUOwWhOmmvOP/YJOjMjoEEFR8rThKbJ75j4nlIjFBQdHBdIeXl4FalzMwKdmp1bRqR0h9o9OxBWZXsnNBXIcIDQNNFQXq1G/h2QUp1fV6yU2ZJrpLKHRp6amlMsquwnO97YaYrYOFkLxQWupSjEA8+u/uRmmgCICgJGZQI0UGcqsZrAHDdjQHDC9RFHue6qYiBRojh9Aikaehj7XkaARBrB/2IckJ/JE2oHorA1FoVmCKTJodNu6Gm73Ukj9Zvr5UDKz3nvYwfIbG7b7T1lG1F8VUkHNTG7pU39fsf5lbpEPeX0dHq0n371Y7MMyL7EMa8vX3Tyv2PPqM2Q+kGUxFWTv9+zarRK4jg4qaIfmgBG9pRkyrVKw1QT7XmTCUD/aOpLG/BOFbT//g1nISNw3Lx9lEA6NDJMFkhXLDw7bD444FHyzVBQO62OPcH1FsRf7NYKA51mDMRKPN/gNmUYGQWi7uldGu+dmpDQYOcA7zAio7w6+BjxhIa2MihfC0MDZSDnSSBWHrXS6RxGap2HbIVdyMhG5x7Ffs1xk3y6BYY1O+4IiLxT0fTE0NjbjRObBYzYFE8P5Aw5I/uCVPuALPKCG15DSjEvPVjolbxwuSrxARnr+GYLKcbC0Y4vhoPZNsY6vtlGoiwc6fii2J9t5ETHN/v7eAu9HV888wGWfB1fwOfxlno6vnjGgyy97viCPo+22NPxRbMdZMjT8QV9H2uxt+OLZTzAjr/jCzAQaelkxxfJz6SZyY5v0kKcBdMdXxw/U1YmOr6/Oz5IPNkwk4IAAAAASUVORK5CYII=)
⇒ ![](data:image/png;base64,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)
⇒ Mean = 225 – 14
⇒ Mean = 211
Thus, mean daily expenditure on food is 211.
Question 7.To find out the concentration of
in the air (in parts per million, i.e., ppm), the data was collected for 30 localities in a certain city and is presented below:
![](data:image/png;base64,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)
Find the mean concentration of
in the air.
Answer:Let’s find mean of the data using direct method as data given have smaller values.
First, construct a table for ease of calculation.
![](data:image/png;base64,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)
Mean is given by
![](data:image/png;base64,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)
⇒ Mean = 2.96/30
⇒ Mean = 0.0987
Or approximately, mean = 0.099
Thus, mean concentration of SO2 in the air is 0.099 ppm.
Question 8.A class teacher has the following attendance record of 40 students of a class for the whole term. Find the mean number of days a student was present out of 56 days in the term
![](data:image/png;base64,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)
Answer:Here, we can find mean by either direct or assumed mean method. Let’s find mean of the data using direct method as data given have smaller values.
First, construct a table for ease of calculation.
![](data:image/png;base64,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)
Mean is given by
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAGcAAAAtCAMAAACEXIXBAAAAAXNSR0IArs4c6QAAAIpQTFRFAAAAAAAAAAA6AABmADqQAGZmAGa2OgAAOgBmOjoAOjpmOmY6Oma2OpDbZgAAZgA6ZjoAZjo6ZjpmZmYAZmY6ZpC2ZpDbZra2ZrbbZrb/kDoAkDo6kGY6kLbbkNu2kNv/tmYAtmY6tv//25A625Bm27Zm27aQ2/+22////7Zm/9uQ/9u2//+2///bluTKjwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACTklEQVRYR+1W2XLiQAyccdh4kyyQ7JLLe9jBbGCM5/9/L63RHL4qRYH8Fj3AYIpp1JJardRXDBiodYzliBz7R+vx07M4tIV+pR/aanyjLa5VLYSjmvxqS0DtanRjk7u/IBS1vnY3VSMcw6kKRWCOoLReHFAxvt7kKJ0gktHMHAFlpbJFuFs2H0qDmUM3FMgn8ieN064iPU1+9yPWQxpH1aDLhz/WiwMKRPDuJBOdlm5//nLFmgWnCuVR9nfZruInYd7q2G6WZshAGAz6m3njk0SkqcckZciHNI14M258pOpDIuaijnyF+vBjoXwCa8dUlzEOJcnTC7U4S1mJHB/d36cs+ASg8H4WDEoyhdPk2V9m05/a9cbNmPl2fxbOqY3Urv/R3rDFM6+P5l5nTyRU/2+0hoKAltddTqfLol2XFdrfLPYOp8lf1Du2E5roYEl88eS2RPEulXfg0DRVS9aOCsWKjeoGw794UrFgfCRFOylR4ODe5vvW4SQwLmHAmdjJ4fbUBp+ccPMarFxtlgxBbY4Akfb9AdvwBJyTsmEctF4ZcDw/VJ+pfC7hDVWBYrh8YmkMt4BgPivfSVwCo1+U3T0BYqmOG8Jx2k4fL4qoO6yySmFWskcIxRumZ4913FCVwpefQA1sqaAR7YP2bamoEe0D9WyprBHtA3VtqfDC7gF1bKm0Ee0n1LGlc+bTtaXz4iRbOi9OsqXSRrRfoKTq8+IkWzorb8mWChvRoSDE3S5rRIcCN7SlUkZ0IDvezCdbOgvOhC2dA2fCliZLqtQHe104aHT2+AsAAAAASUVORK5CYII=)
⇒ Mean = 1961/40
⇒ Mean = 49.025
Or approximately, mean = 49
Thus, mean number of days a student was present is 49.
Question 9.The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.
![](data:image/png;base64,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)
Answer:Let’s find mean of the data using direct method as data given have smaller values.
First, construct a table for ease of calculation.
![](data:image/png;base64,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)
Mean is given by
![](data:image/png;base64,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)
⇒ Mean = 2430/35
⇒ Mean = 69.429
Or approximately, mean = 69.43
Thus, mean literacy rate is 69.43%.
A survey was conducted by a group of students as a part of their environment awareness programmed, in which they collected the following data regarding the number of plants in 20 houses in a locality. Find the mean number of plants per house.
Answer:
Let’s find mean of the data using direct method.
First, construct a table for ease of calculation.
Mean is given by
⇒ Mean = 162/20
⇒ Mean = 8.1
Thus, mean number of plants per house is 8.1.
Question 2.
Consider the following distribution of daily wages of 50 workers of a factory.
Find the mean daily wages of the workers of the factory by using an appropriate method.
Answer:
Let’s find mean of the data using assumed mean method.
We are using assumed mean method to avoid miscalculation and false answer, as xi’s are large in this question.
First, construct a table for ease of calculation.
Mean is given by
Where A = assumed mean
⇒
⇒ Mean = 325 – 12 = 313
Thus, mean daily wages of the workers is Rs. 313.
Question 3.
The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is ` 18. Find the missing frequency f.
Answer:
To find f, we’ll need to find mean pocket allowance by direct method and equate it to the given mean pocket allowance, 18.
So, let’s construct a table finding midpoints and stating frequencies.
Mean is given by
⇒ [given, mean = 18]
⇒ 18(44 + f) = 752 + 20f
⇒ 792 + 18f = 752 + 20f
⇒ 20f – 18f = 792 – 752
⇒ 2f = 40
⇒ f = 40/2
⇒ f = 20
Thus, the missing frequency f is 20.
Question 4.
Thirty women were examined in a hospital by a doctor and their of heart beats per minute were recorded and summarized as shown. Find the mean heart beats per minute for these women, choosing a suitable method.
Answer:
We shall use assumed mean method to find mean heart beats per minute, as this data has large values of xi’s and has a risk of miscalculation. But by using assumed mean method, we’ll be able to solve it with ease and more accuracy.
Mean is given by
⇒
⇒
⇒
⇒ Mean = 75.9
Thus, mean heart beats per minute of these women is 75.9.
Question 5.
In a retail market, fruit vendors were selling oranges kept in packing basket. These baskets contained varying number of oranges. The following was distribution of oranges.
Find the mean number of oranges kept in each basket. Which method of finding the mean did you choose?
Answer:
We shall use assumed mean method to find mean number of oranges.
So, while converting data into exclusive type won’t change any calculation in finding mean, we are however converting the inclusive data type to exclusive data type for better representation.
Mean is given by
⇒
⇒ Mean = 22 + 0.3125
⇒ Mean = 22.3125
Thus, mean number of oranges is 22.31.
We have used assumed mean method here, because of larger data values of fi’s. Assumed mean method gives result to accuracy and ease when data is large.
Question 6.
The table below shows the daily expenditure on food of 25 households in a locality.
Find the mean daily expenditure on food by a suitable method.
Answer:
Let’s find mean of the data using assumed mean method for ease of calculation.
Mean is given by
⇒
⇒ Mean = 225 – 14
⇒ Mean = 211
Thus, mean daily expenditure on food is 211.
Question 7.
To find out the concentration of in the air (in parts per million, i.e., ppm), the data was collected for 30 localities in a certain city and is presented below:
Find the mean concentration of in the air.
Answer:
Let’s find mean of the data using direct method as data given have smaller values.
First, construct a table for ease of calculation.
Mean is given by
⇒ Mean = 2.96/30
⇒ Mean = 0.0987
Or approximately, mean = 0.099
Thus, mean concentration of SO2 in the air is 0.099 ppm.
Question 8.
A class teacher has the following attendance record of 40 students of a class for the whole term. Find the mean number of days a student was present out of 56 days in the term
Answer:
Here, we can find mean by either direct or assumed mean method. Let’s find mean of the data using direct method as data given have smaller values.
First, construct a table for ease of calculation.
Mean is given by
⇒ Mean = 1961/40
⇒ Mean = 49.025
Or approximately, mean = 49
Thus, mean number of days a student was present is 49.
Question 9.
The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.
Answer:
Let’s find mean of the data using direct method as data given have smaller values.
First, construct a table for ease of calculation.
Mean is given by
⇒ Mean = 2430/35
⇒ Mean = 69.429
Or approximately, mean = 69.43
Thus, mean literacy rate is 69.43%.
Exercise 14.2
Question 1.The following table shows the ages of the patients admitted in a hospital during a year :
![](data:image/png;base64,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)
Find the made and the mean of the data given above. Compare and interpret the two measures of central tendency.
Answer:For mode:
Here, highest frequency is 23.
So, the modal class = 35-45
Mode is given by
![](data:image/png;base64,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)
Where,
L = Lower class limit of the modal class = 35
h = class interval of the modal class = 10
f1 = frequency of the modal class = 23
f0 = frequency of the class preceding the modal class = 21
f2 = frequency of the class succeeding the modal class = 14
Substituting values in the formula of mode,
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAKMAAAAeCAMAAAB35l4ZAAAAAXNSR0IArs4c6QAAAKtQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGZmAGaQAGa2OgAAOgA6OgBmOjoAOjpmOjqQOmY6OmZmOmaQOma2OpDbZgAAZgA6ZjoAZjo6ZjpmZmY6ZmaQZpC2ZpDbZra2ZrbbZrb/kDoAkDo6kGYAkGY6kLbbkNu2kNv/tmYAtmY6ttv/tv//25A625Bm27Zm27aQ29uQ29u22/+22////7Zm/9uQ/9u2//+2///btqyGqwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACfElEQVRYR+2XW3PaMBCFJaehjXqH2E7TC3FKipMYyMUX/f9f1j27kmsC2LjDgzODHpAysqRvz56VJkod2+tU4DHWejJs9Cq6UctgPmxIoiveD58xOx+8jMuB25EEzA6MmGt91Tsvi1a35YSY99u0Cj1GpvWmT/I9GO3yo9anACuMptZatTivI/DVhQRpZ1p/vsOIFo2epd9i5cJ0h5wGN6pMQLb5tU26168nqoz1yT0jJqPnMuFxFV1y4Pnb+H8Zz+AyCN6fsfrGPKp0vSrGd5kw5sCSPFbRn5DgbPILHZ1D74AojNEX1pFGwc92X6bYuD+jTU5ZqLBRSI6Rd6xCCFBFc/yVj56YsTBTSpwcOFX2t8gzVavWpJezMcLqz8gZdSReBGHkCZrh32gOQdPzihlTcPNZKWZZa4xsggl8AM9zq2sDdTCGpwvzyUj1+NbtR2J5jM+wehujI43mdH7x4Z4ZBRS/MgKtg+fK2tVWBsHbayTBs29EU0cnA7eXTaRo2xlVdnLpoIQHojUZeUtx8q6W17dCYRq1160jHdbCWPuR1KLYO3T0cFtyjal/ZLJtLdJVW2SsB+V6Tcj1muG8RuQfuJAZJf/IsBgQfqytuP00m2AbMa7Yo4+OvmYa2XaMfJu5uyd0kUpykbOSQTNczRfyIVX4YtflY2FAWZLyqGmKrlyLJuuFnYmhUdK+uN3LhOIE5JLeswnW2VsdTB4MIBdGBz92lkw580soJKpwvlz3zHX5XbYtXE8PIN7TNxCEXhy5Lo7tpQL2VurJ9wNUaPE1ZkbfDxCRkDJ3L/l+iJRHxsNk5RXoaNN3fOH5/jCBH3QX+peJHwrf77f5XyAqVI9TPL8bAAAAAElFTkSuQmCC)
⇒ Mode = 35 + 20/11
⇒ Mode = 36.8
For mean:
Let’s draw a table showing midpoints and frequencies.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZcAAADbCAIAAAAu6Uv5AAAAAXNSR0IArs4c6QAALCtJREFUeF7tXbHOHrexje9jCIIRJHkGF4GtQoWTB0hhu1IlwK4Nq3GpxoFrCVClSk6hB3Bc/IUSpPAzJIFhCH6N3BMcYDIacmdJLrnc3W+2EH59yyVnzgxnyVny8L3//Oc/v4orEAgEAoHTIvB/p5U8BA8EAoFA4L8IRBQLPwgEAoFzIxBR7Nz2C+kDgUDgPZ0Xe++99wKRQCAQCASOj8A7gctEsRtM9iN236DW4qY3rn5tdw24ahEbUd5YIWaUI0COOgOBQGA/BCKK7Yd1tBQIBAIjEIgoNgLVd+rE6Pcvf/nL8GYu1MC///1vgMYLf19Is1/9/e9/F9WupNdcXaqjGG0AY8yVe7fW//znP0PfP/7xj7pF6WbsYwhS4zCh30+Jg9TdfPP54osvDBrdbfHxxx9/8803SFbi+s1vftO9/okVfvTRR9999x1VmyjGxZqui2LsS7/97W9fvXp1MSB8df7617/qQcHr1691+U8++QRO+eGHH47ABNWicjSxWvnvfvc7xJ3VYlUFYGuU716tIwNw/te//vWnP/2pSs5TFOa7v8SUp1DnOELWRbGXL19+/vnnjx8/fv78+XF0GC0JejK0/vbbb6WhJ0+e4JfR7R6kfowdoO9uwvzyyy+7tbVzQ2/fvt25xRtpriKK4SWJIclnn33G96SZ43BWxQuDAj0N0bkAMz05C8rQGoGbwzEMTP7whz88ePBAhKeCerAmUGh9OQ/VaGB2phEgbmbOLk+hpPwtJWVyh18whEG44eO0jjZK85wXYwfE8aXhmMw6Ub9RxzeuTn4JSgAHcy48iBZrK5zrS4RaI0BkpJvgj08//RRC0kB7Dm/nIrNH65yiy0Rd/9f8jVQFBOKP6Ma4pABvoRfxF10Sb3J9C0MYOKjTyv63RKls09CFAkNfCI8/8F8opfX629/+JjoCBPwtaR2mP5gK4S3dnC6JagVSVo5q5Sn9t8bT1KDbNcjjv/puidFFd10VQBA5jd0hDCFavQxKHNjyKQ3maj37F3C8hSjR1tqCIiR/3F/m67VoYHwHUx9iTqyIiOkhpt9qa7HPC450X/bJg1yFUYy9C7owqC1FsTRMmyimdc+GCcIi7wmNWIqexFY8AsF0nNLvEgdqR30Rj5XT+jqKZe0uLzOn0SxKFP68UQzCE3NxFSIAZXVoE1gAaQlWB+kmhxLDOG3pjBJDfSCOiRVHEx988AH+ZZKbM6nf//73vGUuPIWBtEyUmC0+Y4IAWXYID12ePn2a1ZQ/Ag18YnMK6Fvvv/8+A9PPP/+MyvX3uIcPH/7zn/8sqWdpLQIn/r3mL9Ba5tSiqbE7vaIksZWihHD8008/leh75DJfffUVFMGkGJFLsvjPnj3LZvRh34t9gZ1lmtIo9o9//AMiwjzsFQxGd3d3JXLrsRgj+kk/06AnQ/GzCI8eQrRhI+bLtuRimB3TnzhKTB9lgACSZdmVSUhlBj5dECiNYi9evDBZFcQmrj/g+2RpeAXXf/PmTRdZp1eCnrw6PgIa5Qs1gQzfBxyU6Qfxhujl5TKvKXzrLOFshmO0O19vvH788Uf8e+/evVVL4dkffvhBF4Mv/frXv1598OAFELCgCGaUGLdueWccXM2jiVcUxTidNEt4OCThpBLj56+//lp047cYXnR9/UETn9UuvGgWk274sejrfLYDCECG81OOdKQwHkclGtISv0HU03EKtWnYETU2zl8oJAQTYfBiwyhPgi/sDk9gK/wUu9STv/zyS3iU3KXimI6VqHnYMkAbBoVeSD4QmQv7+bGsoJN2kCybw8NUP/thUX9aQhlRzHyLkW9zLHDSb5QGmaXsviT+qaz+bmVwwF3zlYPjMl5yazW7rz8WaxMwxyzX0tfDJaMzV22MRXXSz9NsRTfB1rNfRYmkQUPgPWl2n3l9nTxhj8AvgIXWNP3iaB3hUPl7XxjjtJZfjGmUjRfesZiBrk6+NrbS63EMGbpovSoPxixwXDj0oFX+qwJkC+ymfpt4R3uqAS6MNDFCT42OsfNZ+sjBrVA0o1zVAWNpPXXCWBrr+1efigKBwC0ggG+U2fdWhLBe1u8TxSANMgKynAKj67PnOHrhG/UEAoHAaASGzChHC923/oY5Ql8B5tZ24+rXgh9w1SI2oryxQrex2AhZo85AIBAIBFYRiCi2ClEUCAQCgUMjEFHs0OYJ4QKBQGAVgbooxqWMo6k+V4XeX4zaFvmhY1WRKBAIBAIdEChZ9Spl0J6sbEwpaPZcNcfW0x2aDTKgntWntOKrhVlAU4AUPjKlWIn6GwVrQG9ji+Me3wGuccJfpmZjhQpmnkKml92Q6iXPql+2NcQ16IfiIMqaZlX9WoNqsqDaZ5fKG9KhXtU21NMdrgYZ4hFjhYoZJdaysj8f5OKStB2O1WhTHAsd0Z9v7YCCg/hGiHFbCBTOKLO72/Scjn/LbsqlPWIpB6aemfKVK5T2HMhoe5jNgJqxr/kF5b9dU8Wpox5kcf9jKsApuD0d9QmvfnUJqx9Vk0t2VurttLjLfZRmJKWPLDAJCqAqm0mlTr29VFzOvFB3oxuMsVhzR+v4YOOMMt0YzPgimSk6tPRtJytkZhyGUFTXySb0juJ0c/L2LbW+X2YVZ1+lVZa2yuMWA/RuHazNS/wopvE3ROT6jYJi8t90RqmjmOE6l/plc7jApZv2aWwhWJcMaQmAEcVKUBpdxlihdEYJHs5Vuit4kuwXA9/pEs3Wo0ePNGuo2XQJjxQaQtYA7i1555utZ/fv30+JIvQYYfvfWcW///579Ct8q8W+dzDViFSASGtNjpoS7tPtcg6qAUFHNpPpKTxshO2B0ihCWAmrGj71Ai6gJw/C3CAOkP/iLSj0QQ77K4yiB2gQ7CzUlYPMdOPVlkaxBpiWNrtqYjJmtZY2XcKh4cokvHZiaEn/aZDffwR0XeiQCMGaACfLQXxGeu4l3RE7QK7Nu/qAJbyWSvY2EwrZb4s/AKDzHlqyLCgi8BTr2SEx2t15osK+CAyMYo6g8gbmAZdOSby3MTpFGXptNpZtJP/rCGhWPAwYOzZxkKowDsXbRWZ/vhGNzOl0o1YpnjTM8MeXXMSyWgyvVL40ioFNuORlWwgNaGNJ9YnhDGg/V5/C5AVei1GPoXXGu92kflerqi2wpDgTf7hwFsHSkIG/lzA410o1pTxP7eYEH4ZDAqH2/cGA3osBVQ4WwID9MqzoUyx79kZLoxiOODIRZIvm8D/0f8wm4H9OT4C7630CpHjX5eG7q9m6LXLi2azikAqSI7biQjhbOvSIPPS1XX2jwOMeB4WcHJ6ij1Mg9ba0m3Lqyy2uPuG5ubwQGUssaMi4Den5NTj7xxnu+jUXrrRIPxem3yj1d6L0wEEzj8guCk0XN5qhlqkE5tn+cQqV+J9UUMB8J9WPSFqHSwp0VSPWf3b/+uOob+aJmqhaJ7OoptZdrJZdaWEWSbCMJuaWj79LZNxmnYfDi70nXN3bigqXEDBOO23t/mqYWzVh25L6bFLGb6u8Id2TL7B2v8tyvFU7nqvA6jvvXOqcVNr2KMbB19IhFLVwbBxGxT7KWsALX2u6WESxhndeL7tEPQ4Cm6IYxxd6nN+GtT48qaGGXmKw6ZK3a22LzEQ0qLb/I/6Mcrut99doaItnMetQEKZXbqwQjNX/Xb7EWHab142rX2v0gKsWsRHlg7F6BKpRZyAQCExDoHSlxTQBo+FAIBAIBFwEIoqFg6wgkPLcYvXW9Xb/cEOVPlY1POMsCEReLPJiK2lB9G18jZG93+jnWKqqd3SfxddX5US8xopc//D2yIutwrhDgciL7QDydZrALjEoo+krsA0erCTX0VBpgq0FiNdX1e6SJqNSMaO8sHE7qJby3I6mQuog9IYqsKsXCvba6blBkHi0AoGIYhVg3VpRdmZs3RfFebCT5kpCjgzjNUwzmSnjI0ylyaVxk5K8K/tkUY/OSTFLJQ9iDqsrlO33eBxPQQC5q3fmm6dQJ1vX8rAhCVskgwqe8XO5ekSxc9lrV2mx/R57qvRudi6s495V4TjBeO3BgwdcCYlJGeICskuatEf2eyPoYEIqayYL+XwQYiCG0AiTfVeA4EZ01okKZWc+n5Jttngc3AGcGmsaH3JDCbsn7j58+HAKY92upr1YY3oZrnjD9LW5ewpwm1oLwo762R1IEsVYQ3YDv96iL9u8042lun5Dca6PLCD3v3FUNmH225unshsP9Abe7F5XVOLQoN+4t+zZMZ22jBViLHaxt9J8dRC2OOXkxXETmOBI9KpHPYWyYtCH4Z6ZogrlbFoJR1J4CqOq9C55YjmFxMwRkS4V6dq5v0LYT1QsotiJjHUaUVO6pI28+Cn3zhLL+SpG+oQ9zEazXyRHU2+uChkFqhCIKFYF120VbiP41QSKGi8SvS6lnByuREORWGgD5ymeX4NvAkL6qOvEKK+EuLFQjCi2AwIRxXYA+axNtBH8Pn36FDFCZ9BJzYpBEKKGfIhMGWKFMBaRDnNSQe3rr78GmytXrvFCJatE+3xKiqE5aRoDQ0hiDt+Syu/u7i5Dz3tWz6uVO7L7QOwgOcspYvjq4+5SZn0pu4/fTV5JJ8vFP5mY1wl4mcfx26IRzDg2W89m9+XzqBFDz3OXmC9TylljlBv3likumjZqrBA7kGIHkrcDCSMgjFngRrVvx5LyEzczYc6INRl6T4KM8rAWxDkoJ3YglVh2dJnYgTQa4UvVzyT6xfZIY3aJMVd6+BYnuVhBdikT3oAykRe7ASNvUxGLqtC39WFU2+qb/zSy++nhW1ysa1bAzpc1JChAIGaUMaO8aarbgj7yTpGYUdYiNqJ8zChHoBp1BgKBwDQEYkY5DfpoOBAIBLogEFGsC4xRSSAQCExDIKLYNOjP0nAJYzW5cfTC1LNoF3JeAIHI7kd2vw9jNb7xYcE9VjBce+F7ZPePEPWMFSKKRRSrW/WK9aLYY5Td3c3VGJek5JeuG1HsgFEsZpRHMMpxZahirObWxaAYPK45LypZRLGLGraHWiWM1bod7vd+/fp1j8ajjkCgFIGIYqVI3WC5QsZqjQw2J/700083iFWoPBGBiGITwT9604hHPtMWPkqa75KgJIsZ5dHtejn5IopdzqQ7KoS94innqkMIsaNo0dQNIRBR7IaM3V1VDMRStsIgSu2Oc1ToIxBRLDxkEYEGxmpMQq+9Xizc5YAIRBQ7oFGOIlIDYzUoBhH7jqJAyHEbCEQUuw07N2nJI87KV06QfVCfJd7UbDwUCNQhEFGsDq9bKw1+eix81VqDvXrpWDas6U/ZB28NsdB3fwRiB1LsQKrbR7nko7GPcv/ee7MtBkvizZq+UfESxmp8rMRWcAzcIrXfiHI8tgGBGIvFWCwYqys6UOwGrwBrWNEVToth7UbFgUAgEAh0Q0CfLhhjsRiLxVisomvFWKwCrGFFIy82DNqoOBAIBGYgECstZqAebQYCgUA/BCKK9cMyagoEAoEZCJRGMdCtYC5qrpLTIlAmPVYav5iqjr+FOKsITAbJRZdLktJo01/phPBx3W2Wq/CcF15ffPFFdwVRp9RPBk1eWCo4tN11RZDqlwul9X/139hZgrvffffdUoGl3/EU1nObu/gl/bG25l7lHa0NOL4iWC2FqgBUL8H2qcdXn0phydg+why/lRJvWfX5Ea7y+eefD3W/rFKwF3xDewj+hiSj7Wis8E7Y6hvFJIKePYotKUL76bAFvmY46GgT9q3fMbpx0L7tnrQ2P4rNchUML4aGMGfYgVs6bFGS0cY1TZTOKNcHdUkJagIlG5491CNLioDQGXLq1erga767uzuU8FuEefXqFczHPeFxlSDQy1UwQTOTdyQunOn8y5cvEUoGbZxASgGHwuBomCwCuKVZTD744AMU0/PNEtw2lqmLYthlIhPgjQ1DeakqZdrbWPk+j4NLC4Mv09aVmE5Bs4OOoTOYO3vnPnbcoZVaV0E0hCNJ2EIIw+UckYfeBC20pZwUrc7k6keWctM//vgjKscrTQqLYGzl/fffNxi+fft2B1SlidIoBm/Wo0T0XqjULCjsIbVhCobgeNJAliLABOI1LuiCQKYt9dFHH0Ug62Vc31UQxRjIVkMYQwn+FUthXIYeuhTIUG12xrf0Av75559R/4MHD+QpBE3/Ow8f2e0qjWJGIDg3fmHo4en2zd/pQNyOaQuGxLvpPLShdHQ2tLnRlT9+/FiagKWgHd7Joxu9kfpXXYWBzB+FCVaPHj2Sv589e4a/y4nhSgDXdExIfvkHj6ajs5Immss0RjHOwBlx4dw6tDdMzvHIGSdiSAekr9PjLxkp9xV0M3MsG7S75GqSckzaSra5CkdhemqZbV13RimQ2k5u1c4oGZK03e/fv49ffvnll2zTuMUCu12NUWxpPtwmN2o7Y+cHobOxLhNJbSAc8Cl8rOCgWy70qCspuBvmDa4iE0mZWjrSYjZjPivh/bpEHV47o2TCntkxXkx73bt3D/+iaf2qYzHe2u8yS6KWPpFipq0XiyHS4yr5npp+o8X3e732YvqKJGDdpgi/wIouIxYBlQi2sYyjPkeasnbkpApuxMc8XuIt2XUJVa7C6GAy0c4SS66JkR7KtWMdFTcVonJZXXGm9WJcBiJXycK2NBILrOZWR7gbqlq1t6MImtPZjdMteYX8vvp6ylz43mowwYke8eHq5SoNjsRowmvEknIGMl5m9bsODiWRYbu5jRWCmSeYeYKZJw0+i78EM08FWMOKBjPPMGij4kAgEJiBQGN2f4ao0WYgEAgEAhkE7IwyQAoEAoFA4PgIMKXLK/JikReLvFhFn428WAVYw4pGXmwYtFFxIBAIzEAg8mIzUI82A4FAoB8CEcX6YRk1BQKBwAwEqqNYFwZqs5NLb9Eye8u5yXzi3j3NApyyPsFkl2esho5LFMy4RT7riQaa0WvybR7BVUAqvcRVTfG6w6XpqlOmbM0Tkbaumeu3cKVUR7EnT55kgTDLhZ3d3fR4zfeSsoiY1b0T9+6BClHTt5qtuSROobQo5tChdPeePStcMjpk+Pbbb/eU5MhtTXcV9Kznz58vQfT06dMR6L1580Yv5YcAEkYRmHRYwLJ+HchQTHZ0ooZNpE+F+yj1d83uDNQA12zW275HobwGHVJXn9LUwJdnrPaNrrekNOyYWYX6mAXKvWVPV9EbxdI9QJpveTSq3GybbUWf3cG/9XkOhvnal9M0UTEWY70XYKDu9Ua6PGO1+ErW6CCxgj+YDba9sL1YPbWuUstYLSSmWc4ykpIyvhzkSqkvHj58aAhUykWtiGJ+pc0M1KRaJHWJXJMPhlpWFWyOcBTOcGtpiMutEiUvgMAWV0HQqWKs7gVXNivNzliYt3rx4sXSQIesjeT5ITWhyRQ18yT3iWLNDNSYyYOuWh9RoTkXMeDU0+xepmquBzZGsPbzC82WaJYqHjwgAttdpZyxuqP6hvFUT+tKDpFBqgv+nz1nBEEQ2dXVI07aPhP1iWIaR81Abb7apOT65ClbOhYBwGEY7CQsO9pvtSoIDzNAHk3dmz61SkO82lAUODsCvVylirF6OmgI3OiqyDCk8Q6xCcl7DFZIpe1cbd/x+kcxDhT5jRL66HBu+j+GqejzPld1ypY7xVrwS4wZEcIQo0WANhriKfJHo7sh0NFVChmrO6rWPKPEg3jHI4Sl73iEMHRzhDA9WMn26+YRwJAotspAzUVGUGyVbj87f+5otpKqYCGEMFhIhzA82EBDXNJclDkvAh1dpYqxuhdibTNKTCQRwpD/SUMYZmOITZhImvkWs2Ng7hfJwbjdTltfvtJCvlGalRa1DNRcoLDECYlbIhJLjj5tW7eYft/legL9SViXqaIhHv2Ru61+X/0lo0tbo0+lblNq3FMOXB1dBa1UMVaLvgwZWfWdNRBb4GIuP7vUhr6x1H953BybZsmlXpaKZ6zwzsoO36HTeC+1m1s+KEtffLMrOcoVa7aEr3V2lKsd5dqM1Y7R9XoxFjNExs0WOfKDjrd0dJXa9XfpNyVNL55+NOzYrbLDQEau1ENQeEmwKpGMFYKZJ5h5gpmnYkIWzDwVYA0rGsw8w6CNigOBQGAGAkOy+zMUiTYDgUDgRhEIxuobNXyoHQicGgHk3UT+yItFXizyYhXdOfJiFWANKxp5sWHQRsWBQCAwA4HIi81APdoMBAKBfghEFOuHZdQUCAQCMxAojWI+G69mniWPh7+ZwJTHvg3R/WiM1dwspS+z7f7CjNWrFMywWjBWi+tOdBWfNpoSDmKs1pWzm2jKbMNNb/gg9mas9tl4oUkVY7Uw1eJDA9bsYhOWUc+s3m7b6d7lrQBSJL2FgtsmpOZrM1avGh04BGO1OMNEV3Foo0W8QYzVqB9hC5QVst9AiCsQN4XPnduMsB9ZeMrmMFbryGJ2z+nthA3bRwBEMFY34NblEYBfWI8xejBW+7jtyVhtJDFbJocyVpdvpD0EY3WXoU1aCaeThi5iUFvbqwUDnDC91dIQb2/9UDUEY7Vvji2uUstY7UsylLEalLar3IcUD8N2zGPIe3EIxmrNxksRGxirOWcG77NewMbajsZYLRkiKC4D5ltjrE6NfqioehBhurgKesQWxmqHNtpHqYFfDB1fd1j03JSvld0ZfHzCxDWfsTpl421jrGZ27MGDB5rV+5iM1UL3iOSC/+HiqozVJRTMB4kjc8Xo5SrNjNUObfQqMrX8YgxY+FemtEwcm0DGuwx2Pid1G2N1BTOPZgLyOb8kTUaCMLmWmFuctNogUiSdR4B4hYkhFNNze02QxBrSX8prnlWyRH2HKKo8LTJLwb7tlsDFFru4CllSy1Vgf8l2tBFdSesoQkKApfgg9GepMFXiGSuUrrRgJMqy8aYBvpCxevXNgAIHYazOinojjNWFRi+x5s2WaXOVWsZqhza6EPnaGSUXD3B6KBdCFZItfovTGKuX2HhTcVcZq80jGDwvraU4AmO1lpYcu/fv38e/t8BYXW70wn5yO8U2ukotY7VDG12Oee2MEjVjqAiyad0EBmiI2tlG5dYcxmqHjbeWsRrDXc2VypplsYkeKx6BsRpG0iyUNJsMnq/NWO1TMOsMQy03afkU6WgltX8a2Tq6inEzNORPLR3aaBGyaspWDjs7qcxh6TN8HC3qqSWFlJonMFb7bLwm7q5C4JQ37LpVPLar7WYLOH6J8ubs65TU/MKM1b7Rg7HauFNHV6l9K2QHPhJBhjJWAwSd/tbvePOlS3NVEzotWFVPN302mHmCmSeYecqnXLfuLRVIjSwazDwj0Y26A4FAYHcE6r5R7i5eNBgIBAKBwAoCEcXCRQKBQODcCATv/rntF9IHAreJAD4OiOKR3b/1fG0QyVdFgYCrCq5BhSO7PwjYqDYQCATmIBB5sTm4R6uBQCDQC4GIYr2QjHoCgUBgDgKlUcznFK/l3RddScakibqPxruvzQI5NYkQb90s775zeMIcXz5Sqzu7is+775Pfb4dN91l9hgZqNmdWmLZ68e6XMvOYLVF6txR3ElTxh2jqEiimt/UM2u3lbE6CACVblygYLr1V4tr7KI3R9VY+bC7RG0rMZroSPE9apsRb9ncV9CDNxqP7lNnmzG1SVdt9fEvpUMAtR9KdTdMmaEzYR5ndMia7vdqiGMmGhHJIdpCWOErHPlDSnOxL1x7AH/WWN+jiM691FLtXVSXqsy2fSgz1nE73BgxX4TqCqzhDgSwjWAMOeiCiA6jjJIfj3dec4m0jUp4eJOzPbZXs8xRm0zjiBeYhFY9cN867r6E41+EJ49yml6v05d3X+mry++04aPYh1kbKHdLqO9dM3v0spzhlreLd5yFO4Lle0vNQvPscYfHUA30F7z7QcA5P2N5JTldDL1fBSKc7735Kfp/CW8uSWGUgnHQnYa4v735pXsyMOTGFTHk29JRwiZw6nZiYGaVuiIPzlAyneQCcfRBNOBXqyTLlkZxClrHar62v5F1qKxTYoUIWm3bMtnRRbUQlDlzdXYWJyFrSap8VjnasZf5xkIR4OhRwRpl2f9OXlxirCwUzVmiMYv7s2uHd54Pa3Z0oBux2SPY7fonW0xy2H8WWgvuIHtWlzpIo5vDuiwxtudEuKuxZyRJcg1ylNoT5LxsC5fe4BjA1Dx0pw8z7jL1efwCcybtfOIBc5d1HmknmjNDw+fPn6QoGtjWddx/iiagQGyLhXx6D1EamXojhcYoF736hLbq7yvF594kMDzPj9ejRI/xy7949AQ25QsZinUHqy7vfOBYzc6t0vlm+8OLIYzGjl9E6+41y9Py34VXpP+KPxUre7YPe8N017VJhydAVDW13FT0KKxmRldCLEwGoMO5rMjq+7gJLSaF0TlY1lm+cUTqc4rW8+8aZTBTT8h2Bd19Lm8bua68XczqGf3hCl3hxzEraohh0qXIVM//iNNAZGTi8+z75fV+QDbO+n4iYsF7M5xQ3Q+4qaEwUOxrvvh/F6F6ifmFusgqf0YWdbunz7m8x+milxtXfHMWqXKXWkbJzXg64VsnvN2KlSffNRCQ9mQFy6sRx8O4XJivWi90418qNq7/uH++WCLhqERtRPph5RqAadQYCgcA0BEp3g08TMBoOBAKBQMBFIBirw0ECgUDgfAjwYyuvYKwOxuo4j7KiD0derAKsYUUjLzYM2qg4EAgEZiAQebEZqEebgUAg0A+BiGL9sIyaAoFAYAYCLVEsZeOtZax2yh+NsTql6sacXNPyXpixWhwS+sJkS/6Z0o7P8OT5bR7BVdA3Nf+7AYXE1oZUeiNwhpOa/9VN6AKmrV6M1dVRDPJh83aqudkegQ2iPjp+ebOeGNvLN2K98XHDNPLVV1+xQnI9UlqyGsCVN7Z1wMefPHmyJBV5AQ8o8yyRJroKbJHtm4QCL5tPP/20Oyymq3KrgPCJonfIgn78gYgmApBkkI8DNHgRJGwTry6KoRk4tNCKtzV5maeABrghha4WoQ1RjFRwl7n4InXU+fjjj7kh7jIqj1BktKtwGOhbAWFih54LLlkMUD788EPAiKEfgpp0EP6BH/EvA+7Lly+JNihI8dSrV6/awK+IYktsvG0NX+CpW2Cs5qvSbG4V252Idnyuv9W6Si1jNSYrtNRSIOOYSOYQg9BAsEZsAp0963/z5o2RB46EH3FrGmP1EhsvJa5irF4tfyjGakiLobiIJB5wa4zVxvVXaccHdZWDV9vFVRCPtjBWG4jKXzYbGaufPn0qAzEOuMjEpy+mXPoyVpeOxQAE5FuK5eA/k+kxRq0wJMeNS5dTHk1IVdguj9DuZCt3cGh5y8m7zp9hGQqBHSSc0gTsC9P88MMPU1o/ZqN9XQVRjIGMXInOIRU+GghMGGEUPq57n0l4cZLoXJw1y0BsqaSfMW9LKxdFMQDhH/ahJQYQiHec8cppIxzIZEObLm80B3CIiU7Ccn9vZr91YvQtZIjganhR4R0z/avL/g5Q3uJ2V2Eg2xLCmMje581qBmJLQKWjM12yzaOKohiacdh4U3FXGavNI1I+rWo6Y3UqqoyHb4Sxeskdy2nHy3v+lUqyQ3Lq1OYqtYzVS+jhzarzIYhr+G921NM8o8wOxLL9mrD0ZawuimJmnCmUp0uDw+x82HFQp3x2/jzR12l72oCfk7U34PXb9jKZqFFD02bqxKQyP6ivzjsamjvpIxtdRSaSMrVswAHmMBNDVEL2xKyjNs8oswOxBw8emGEgppwI6JCBx1byOEted3d3/jDNU18riXIlxI8pp3h6uolzqJfPcK1lOAJjtTk73pxbVUVDXILt/mVKjL7Kid79WJ39cShs0YGro6ugFbOgsoR6X79OltSRKFaob0kx5xQO7RikfpUKJzBWa2VSoU2YXNXcKX80xmqfqtt8264lGl4FaocCfhRLX4BZkSKKAZaOrlLrSGnma+lEwRFRzI+w2oWM8wRjdcP4Ov/IjXOt3Lj6tW4UcNUiNqJ8MPOMQDXqDAQCgWkIFGX3p0kXDQcCgUAgsIZARLE1hOJ+IBAIHBuB4N0/tn1CukAgEMghgA8F8nPw7gfvfvDuV8SJyO5XgDWsaGT3h0EbFQcCgcAMBCIvNgP1aDMQCAT6IRBRrB+WUVMgEAjMQKA0ivmc4rW8+9RUPyW7EY/Gu09RtfqGgf7CvPurRPIzPPbobU5xFUMe41DItMHHozaWWP9I588r5dHSD7a1vv5U4T5KbnEwnOLy7Oo+O7PzgLUJIbe+S1LdHXbeSBOrzVGk7M7Qa++j9I2+p42O05bvLbNcxdnJ2AU6rTW9glvKcZmmTb929lFuEcxY4Z144ViobxRztt0dLYo5/sFbessb6XC3mGf/Z5uNvr+oR2jRgWuiq4yOYgZ53X/xItfDEW4mZXn9N39xRkJVxjVWKJ1Rrg/qiktg9Iue/+WXXxY/MbMgTjTQJLxalFoy9ZlqRNvjEejoKrW8++OV+18LPBNE+q+Q7bAEKXd4mpHDu99X4LooluUUp0DlvPvo/IjleqbtzKXn0lVDL1KG6bm9nDd1I7z7jtH7+uLZa+voKhiYNPDuC2+lT9SlM7nasVfpvZjIBo0zxCM9meZQ0+Z7+/Yt7y7x7ne2dWFeLB1SLg2tOSVcyqChHtIMSZrJyZFxnJxNn1WNP/3CS4rIGFiTnOjEhyZIYmHDoNRRyHFV+errdknGPU6SU9TsIIBbfV2FjDeFzGKmIy8x82wHmb2SHTxNNOmsWZoupzrbZTBWqBuLSQR1OMVLePehiZCCIqgvkesfhHf/8ePHojgPnXQOzrsw7/4qkXznF+wJq+vrKs28+wg0iCbNh9T6wKNX4m3tnxJCMuTstTriazB7YxTTnOJpqz7vfspB7pDrT+fdR1TCzFHrCDNwIN1Gpt5gpIM84hv9IEJOFKO7qzTz7t+7dw84cFqXXs0zymxPx4+kldfX/fv38V+Hd7+vmRqj2NJ8mML5vPukq9cvCodcfzrvPs6+NueV4Q3J/nxrvPu+0fv65Rlr6+sqW3j3yWfPUJJecODsnM4/Y03Xozs4Jon6Na+Py3V49zvbtzAv5nCK+zz6Wbz09NgsP4F68sgRePeNeMyLyeqKa68X84nkt2c3zliD9k8jf0dXQStVvPsorNczpo9vgdrv4GdaL+ZzipvIWgLZEuX20Xj3JYVJHdPcpE6E1dKllwA1uozTLVeJ5EfLdsD6Hbg6ukqtI/HlKlf3RYsm22vE036SfovTgvUyqLFCMPMEM08w81TMb4KZpwKsYUWDmWcYtFFxIBAIzECgMbs/Q9RoMxAIBAKBDALBWB1uEQgEAudDACk2ETryYpEXi7xYRR+OvFgFWMOKRl5sGLRRcSAQCMxAIPJiM1CPNgOBQKAfAhHF+mF5kzXJdhYQttwkAJ2VFq6X6WwunRUbWl3J2n1HAFkxbFZIyro787uuSq8gZbHsmtK5nBa91ukdth7AviQbKTrSS8yEAmaJeUc19fpn4wNcL85rnABZXbbAtQpOSiu4+khhAX8BM3cdyKW3AZj1tAZtf71roWwNxYwVSrle2dIS42uWbCd1L4fHlXuSIJwhhnZYYRuUr/XLXk0cuR6nW/IzkEOlglsOBdMWrQ0djY5WxgkbiGu2CLYFrtV20Y8GvbPNZjJoIQ1pph1IyMAkZgW8eqV++qB0WH1rVdONBfpHMaptoo/ZU0ahl6IYC6OGNGZFFNto79XH/W7pBzLt7qsNlRdIX5bac8wAMOUNL2+ooeQWuFabM+zPq+WbC2g8017pdDq9cdjhqm4WrPBBY4UOeTFwP6aczmB9gLe9ePEiNyOxv71+/ZqMY6Bnev78eckjUWY3BDgGT2mh8LUbMpAJdgRpFPiORUdNq0tKVblFojpSKRzhWoKLRKmayoUpRZEZBUCYDP8n/6qcCraPUlowmBusU2m7KAMJhVnM4areR+b/taKD3+p7JjujxFPZ3acco+nh6NJYTGJ/Wn+MxQrfTs3FVo3OmukxppXCsZjZ4a9dfElsSbjgj5Q1wfjbkgc2Y+I8uAUu4sDKs6ynhWMxk6vSeGZP6krVMdNwMRBKpgzG/BGt6NzCEsvroAxD6nj6lw5jsY1xl4eJfPbZZ6gH71gAisHdxjrj8e4IMJDpsYNpAgeJ4sq2+/333y/FhSU5eQgFnAFjPdDJa3Lg7COGybK7+rUVZuECDlAEYy4AhYGM8HkJ76ZuxSHpA+HwEp5CoewIjK+f6HGarPXhw4dEG/bFYFAz1rKeZ8+eoUWMglFgycosmTIm1kLXUH5+FAP7s/ZRAAoD7zycbgDu1h7hQgpnFICuhasLLLA+vxtI+EOvcwIoGs3OgLoI01bJElwIBHDvJ0+e6M+swrup28oSpbYJo59CDEKcArYS7/AL5EGQItq4hf9m13mQXB53HTEcrurtwi/V0CGKIYTf3d2lDfAcJ53CyAoBu9JHeRGj46Q5xkF/opoxXsaYCB7sxCl0hqUlY+nR8WLuLAjIk+L3Tz75RO6yzzN3kxJD48cpnWfJgiVw6WezWUWEcnMKvTwCqPXZRdkDurKyMWAhTmlskbzWS2pwC/81/MZpbUv05UsEs0O9vUMUe/ToEV4v5qgC2CA7NDXKcDppSNdiUjnU5LWVw0aY08Gzm4datTNK/7AFEEProTodb0rnySLpw8U8Ly5A2jzhaJtRYnjFMaAOYVAhO59dchL9mcXhqq71sa3lt2f3JflnDmcrWS+WXTapPwtEdn9Eirrc6P5henA+yeZipNYxs8sxl8ips9FHXi/mw6WXKUAjUVD+0Nl9qNlxQS/z91kKWXY3+WBiDmrTVjBLyXyu6qF+C4Hf8eFyh0bJpVWvnE7rgJr9amm+UWbXlFEeVMVVeVwKa66+ABlE+lZ+/Noc9WkgZx3muChmTH+Ktfs+XPRk8QdZLk9N+fu4KJYd7JjIJWX0h06fQf6Ua/eP3ycbJIwotgTa0g6k7Fu971iswY77POJ4SxVcWlo93tFhruNYbB9wdmvFWCH4xYJfLPjFKtIywS9WAdawosEvNgzaqDgQCARmIBCM1TNQjzYDgUBgGwLMnvOK2cQ2LOPpQCAQmI1Ah/Vis1WI9gOBQOCmEYgodtPmD+UDgQsg8P+vg48TjK01bAAAAABJRU5ErkJggg==)
Mean is given by
![](data:image/png;base64,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)
⇒ Mean = 2830/80
⇒ Mean = 35.37
Thus, mode is 36.8 and mean is 35.37.
The mode shows maximum number of patients admitted in the hospital is of age 36.8 years approximately and mean shows that on an average, number of patients admitted is of age 35.37 years.
Question 2.The following data gives the information on the observed life times (in hours) of 225 electrical components :
Determine the modal lifetimes of the components.
![](data:image/png;base64,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)
Answer:For mode:
Here, highest frequency is 61.
So, the modal class = 60-80
Mode is given by
![](data:image/png;base64,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)
Where,
L = Lower class limit of the modal class = 60
h = class interval of the modal class = 20
f1 = frequency of the modal class = 61
f0 = frequency of the class preceding the modal class = 52
f2 = frequency of the class succeeding the modal class = 38
Substituting values in the formula of mode,
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ Mode = 60 + 180/32
⇒ Mode = 60 + 5.625
⇒ Mode = 65.625
Thus, modal lifetime of the components is 65.625 years.
Question 3.The following data gives the distribution of total monthly household expenditure of 200 families of Gummandidala village. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAiAAAABZCAIAAACIWQhrAAAAAXNSR0IArs4c6QAAE1hJREFUeF7tnT+OFb0SxR9vGQghBKyBAMEXEAALIJjJiJAgRpAQkoCIQSIiAgIWMDMBASAC1gAIIcQ2eAed9xWFu+12d9vXvndOB6jp6y6Xfy672n/GdeLXr1//0SUCIiACIiACpQn8t7RAyRMBERABERCB3wTkYGQHIiACIiACVQicsCmyEydOVMlBQkVABERABI4TgT9uxTsYrceM2gBcb/9k+ldSGhbpYYSxCMaYEOFdj9cz1BTZep6SIAIiIAIiMEJADkZmIQIiIAIiUIWAHEwVrBIqAiIgAiIgByMbEAEREAERqEJgmxzMhw8fsHz09etXkLhz587169erIJFQERABERCBEgSyHAy6cvTs/nr8+HGJ3MvIgHrwN2VkLZVC5xe8zYe8AmLnz5/nc9z4t16/fm2v4H6pOiPvjWpoajBT77M3rKG3Lq99VwxjSnaC0RtPYI2dYExoWJZhzHqLNCiWwjfPTvBa6YYalsU7AyM24PLCO3Yf3Fy7du327duxXzf2/P3791Dyy5cvG1YvQQaaUCteXjHoiSevXr3CQ3+P/4InLib29xSFf00s73OuhJIxDSH23Llzjx49GsrfsIbewGBp0Ioq9cOQNWWtwCvZFUZrHX1iBMNRDcsyjFnvynbE19GiYZ/WtHuz0lENy+KdxOj7oj994gIHg1eso2QZ+F/0WbiHibPb9WnYZfCy5soeEDU32lObHP5KA8VDy8veYhGYu1GwPtR6K6Zn1+8739GuFmkSZCwXKu/R0xDtCRS28poXMQWYDAp4VriPqTSs40klhxomzG7DGrIurAFbWbpiGFOyH4zeKmjYvk/sxxSpidewLMOY9U72jJON3QzSOhC80puVstvxGpbFO4nR90VZU2S+Bw9688+fP3PyB5NUV69ePTg4MDfwzz//UJXDw0ObIELhraE+e/bMDzNfvHjB9EhjU164OTo68hYZKHPv3j3/aRlT1Z4/ePCA0vb29rCcc/nyZY4S4H7u37+Poe6khMwE796989NfZ86cQUHwLrM4efIk5fCGD9++fXv27FmTj3s8ycxucTKUmjM/xnzzGqIuTP/v37/zCxFXVwxjSlLVHjB6G3j48GGfGE1Jr2FBhgnrXdxG+CI6q/39ffR4gZx+rDSmYUG8cxnmOhg4g9E1GHSaaFqYu0dn/fTpU8sexm0NEl/u7CjhZoLncCr2ir0OR8WVfFzIF4Y4t1SJ9D7HJ0+ewDldunQJ6dGb4/7ly5cF8yolCjQMfrBmszILtBb7HgHqxUtrpTRE7wBz8nW0soD2eikNIXCoZFcYuWKKr7phV7geZhGMoxqWYpgoIz6hFi9wotLhXTgyqHetwZvWsBTeuRrmOphgDQbjBlJGv4wRCazZe5egAvDxbk8wULA6Ro+WU1WnTp3KSbYsDTQ3fXC/TEjttwDZ3ECNXoP6Yzpu8YCpiIZoIRxQ0uWXvYpoSO+SVrI5RswicN5muOtkPdIiGCc1XMMwUUb0UdaO/Hg0B8vHjx+RzPoK3MPfFN/IugZvvoZr8M7VMNfBxOoADg2g8e2PYUcszbdv3+wnv8aAyrYptUQd//jxI8cClqUJHGfCTc6VjxlC7wwAgYjYe/78+ZMCecOHV65csaEb/ot7PJmb7+L0Vk1NNMToHh03vj+8d+mN4aiSAfC2GE2ZCxcu0B3i394wUkmvYUGGCetd3DTwIj6p/doDnsCFs/vqBG9Cw4J4ZzM0angztnqT2EVmaypc1acEv8ye2AiEn/hKsD3MFvDxk98QwtX+YJEfaXx6frtZMt5zqZya+H1ZftcW1RhdVE+QMWLDJfSudkAZFl/F0NnK23afW7Apy5TsimFMyX4w+k0lqFmz234wxjQsy7DqLjIaJx0M7/vBO3SBfFIWb8xNjLqS3F1kgeNix2R9t1Ee3dnlt9/wLbv8Vi6/f9EPdCxxzMF4mSwkXudb7BRiDsbUtixGtwWnHYzfh0Y5BjqxRc0WYH2TMzdAOQG3dL0mlIxp6Hf0DbPbpIbDzyIreycMA7v1FdQPxmC/pTeYTjDGNCzOMGa9szrHROKgvXSCN+ZgiuPN74v+igcz2oqGjX/yCdaKnz9/Xm+1YFKBsgkw8VqKTFnFvLT+lZSGRWpfGItgjAkR3vV4PcO1azDrtZEEERABERCBnSQgB7OT1apCiYAIiEB7AlWmyNoXq6gG/Y+aUdz+lZSGRaxSGItg1BRZPYyaIqvHVpJFQAREQAT+T0BTZDIFERABERCBKgTkYKpglVAREAEREAE5GNmACIiACIhAFQJyMFWwSqgIiIAIiMAMB4NzfO0oX9wsPnm3LXRfiraaKHcREAER2G0CuQ4G7gRd8w78cT6KgEMni4dYVkDile2k82jEKJ0CEq+sYv96/1GHE4XtKCDx31oGJoo2ZQGumgV1Hj2hbHjUDAoyjFU8ebBPnwl4Mk9+cZA4URAFJM6s5QTG/qMR84A7BSTOqet0e+GBe22jDqcPGUuXcag80ncSenw0aq2duNgkfHvWYZfQLDhmPxaHONFx4ycLiozTJwMWvouhcPPNw1C1/Mk/9+ntwMrgiDdvNzh0r2A0YjukMjDNmNlBeVPSB46tFDK5/4DE2xWNGLV8nAMST/qYtIPpIerwYgczqnzCwWy+pY/CbxjUOWuKDDFBb968mRgzWhxi+InE7BNDwuGyeGUxmQhryJRAg7cYJYUh2/gViRZuzzEw9OkRVoRiMRVmPRf6bh8OGSEcFgfXmjVR0EMk3f4DEm9XNGIYwLENSDzL+IeJ+486nJ4ZGw2ZzFd6aOnUxGabLbhUw6DOWQ4GiqbDSlqMWwTISqzT2Ahm0kxtRMKu59OnT2zVGHkwaj3CCmF88ObNG9zDvQXpYcd4DleEAO/MCy7NR7JCsKMNrCeVClM6iSszQb2AxJkKTCarF414MuvMBFUDEmfqkE7WKiDxpPKbiTo8qcayBJsJSLxMN3sLvaUNzhiUa6XA9a9nOZgN9MWJknhMiLJs/tnPgNnngw8Ti1GOPS8e3HQu+jVhSufmNZp+MtZvkVzWCJnUsDlDlG4y3O8aAkXendSwFcb8mL5FOJQVkq98K7xBeTlL5KdtygLJlJblYGx3cqbQssm8IwkWTmyqLYjNxXEPhiz055BweHjIYU2rq20k3f4DEm9RNGKY0LENSLym+fQfdThRuk4DEsc19sHXWwZ1tiEVVI2tfWFiKujBY2EifbDkQBrkeyE+XDHvLeKyXxv3kV99LGQuz1CgT8P/QiCcShAWM1hJDrYtLF73s7WiAGDDMKVBWfoPSNx/NGIu5Pr5B6vufiLmbiYg8cpFft/hWJPcMMOVjR2v+96sn5buDcC3qQ3j9T1hmV1kticq38Ggkix+KmNoewfjHbO3hiD6r20bDVZ3+IqfWwuGPgV3kSkg8WSPwwSJL5jhd5jfUmm/Dr9y+NMGwk57c2WmMbMMLG2Tkac3FpA4XeOJivYvjn5xkm1thmUdTMOAxMNPSWssQaNoFdQ5Nx4M1jbAkQvstS/MyN26dWtyp9liNTB4BP384vQfgQMo+ldSGi62WP+iMBbBGBMivOvxLokHg2+K4n/9vr4kyyQ8efLEdqMtk6C3REAEREAEJglkLfJDCsYT2EvWdrV/sjA5CVCEo6Ojp0+f5iRWGhEQAREQgcUEcqfIFmewAy/2P2rWFFkRM1NFHx+MmiIrUtejQpZMkdXTRpJFQAREQAR2kkDuFNlOFl6FEgEREAERqEfgrymyetlIsgiIgAiIwDEhwD9L+D11/+fuxJ/7Y0Ihs5iams8ElU7WP8b+NfzdYrtvp/1rmDDU/pXfLg01RVak85QQERABERCBkIAcjGxCBERABESgCgE5mCpYJVQEREAEREAORjYgAiIgAiJQhUB7B4Nz2n0Qlyql/Fco/oyf4WT8WdZVc5RwERABETi2BLIcDGPk+Xgq6KkfP368XdSoMM8f3cypndvFR9qKgAiIQFkCWQ4GWeI4fcSjLpv3hqUh5NfVq1drZGpBNmNDMfjjHo5x42DRfygg4J0p3/CLgYrZ5evIBp34taGGVCmmpNe/YezUBMZOKjrBEJXbgylO9g8kOUzm4beaIPH2yfvmTSYrHgyDtfgYKj4mmL9n1AGGaWGMFkYDw8UT8q1iLITMMFkQNIKvWHwwC57D50GMEL6LxJYpn5gaeG6BZ9YHMmFeJnA0cBYKziszu2XJUK70iwDF2CQ5UZ6W6bA4TAgYWmgfzxBGYmx90KQa6qUj1iQq2ts8hcw1sFnFSVR0DGMi3tSsrDMTpzUcbSye4QYqelk8GB9SZRiIpXYDtxwnW7pPad1sZt0VSeY1nOFgfAuc5WCoNHt83sPIzGGYg+FPkDwa2jKIoZmoTt9D+XvvCWZxTNdoECgzSAw9GfCutv1NKkkFvIOhyzEU/IaYRWZW4syGwWY8Khk1GISimqXAZOJJhiaBRsv/9o+xHw1jjYUhaA2v714ma61sgkkr9VXPrBMWW1Y3SpvUkMl8H1tDjYRMr2HuFBndw4KoMBY3jEZDOUGMaDyxZAg1huP08QRDTticf/78+XO+juvFixd2H9w8e/bs4cOHfHj37l0Iwag2lnj98729PRPy/ft3H0aTkdN8gvXZLZAAkpjeRLSF4N137975ibszZ86QfNsLdecZmjKoxMPDw9OnT7dSL1bReA4b484RXDA/WF0rJS1fj7Gfio4xvHTpkl8WBc+GFT237j5+/AiLtempHibDaYc9BCWZ52DQ3aMPKjLDGMQZtUoNDMuq7f79+zkVT91OnTrFxLTaHz9+5Ly7Mg16QChpng9z8VXjcmZqC63gXfjh0/nFvSTwIoEv5Kz35cuX8YHS3FuDYVDReMIRKi8Ms9puIYlh7Kr2hwxNPegPhj1UdCYxLO4ipX3Rw8E0XIejzggO2UlMxXkOBqrjy6hqaEsMAqxeg2ml4Tf40AICjxL4m0yLWZAMDQY9IAbL+Bbj6+go4W/oIHHDj9yqY6lRtfF5hed+/Rz+pnkDGFX14OCAM07BIiqQsvViCNt80XJY0VDp7du3ME6bwWiLN4ZxgVVXemXI0HsX3KMIlbKuJNaPWh48eIC2XymjHLEc6/cwjIa2sx0MvizQlvz4A3DRwFhym5vKATGaBn0xPvzxE2cefIeS2W7hulHHFI7oyPBS1ukv1ir9Iuag4F2grc/Iz1HaGkxtTYZ6YtDpNUEC9OBswMFEZb1ddrOwX7hwAelHPTE2AZqlzZJZKvFoRYObH7LcvHkz50uolEoxOR5jVxU9ypClQE8CklvnXTC33EONmyWgE0aH03YYbcrMdjB4M1j/wEwfHCa/ka9cubKs5dgnNtDYugs/Wu2nTOHQx/a2YkKvdt1jPAd/BlU7qdF8/uiD4BS5a5mTtuiJ8l8vmNJ/AL558waS6YnxeeE3VUPDTBsoqJuJilU0oEEx84gwhkq74ScLFcPYT0XHGML80MzRM/awbDDJOUhw48YN/ymMLwx8484VUio92gt6Y+tCS4ldLsc+byFiw5sNtiW7NJkh+uHO6ea7yHwte/X8zsuqG7TSu1+CBmnaBgt1DTUcXcQykms2wc9tBQlrjGG0nU601YYYY43FA2Sa2rsuY9gTeH1joZKjhlp1K2a6HbG91K7fSYv1ZBQPZto349uq/0Xy/pWUhtOmlpFCGDMgLU8ivMvZ/fumZ7hkimy9BpIgAiIgAiKw8wTkYHa+ilVAERABEWhDQA6mDXflKgIiIAI7T0AOZuerWAUUAREQgTYE5GDacFeuIiACIrDzBORgdr6KVUAREAERaENADqYNd+UqAiIgAjtPINfB+MOs1kDxAZLxd9r2t8eQ7/9me00WelcEREAERKAHAlkOBgc8WPiWHpSWDiIgAiIgAv0TyHIwOCmo1BlQOMJy9K/i8XCLDujuv16loQiIgAg0JzDtYDB8sZPnManFY+nsstOOGbTDB9ZG2SyZTX/5KTJfeD9F5rPwoQEY6IKX5tOam44UEAEREIE0gWkHg/NNLYIpDunEmcF22BkO+8Pp+v5kdRxdzl8Z4o1hUHH4mp2fn1MfDDNMOTinlr6EnowPIRZB+nJEKY0IiIAIiEArAtMOJqEZJ7V8vEiLcoPVewupdvHixVj8yqFwOBI4GJsugxBGB4DrsoP34eS28VjvVnWsfEVABESgCYElDiaYB8vUOz/QMoM/8sIIhvLpUex5vrRM9ZRMBERABESgLIHZDgaLIpgW8/FFyioEabZjjblYhDuLSosEVcM2Fy+RBIqACIjAMSQw28HQAZBUjQjzCA+HPQW2ho+RCn0JVvht1LJ1sSOPoWGpyCIgAiIw28H4AMkIcVqcIDcR7O/vczYM6zGM44t90tw4gAuBkLcucHdxUBIoAiIgAp0TUETL6QqCS1NEy2lMUyn6x9i/hmDcv5L9a5gw1f6V3y4NZ49gproR/S4CIiACIiACvwnIwcgOREAEREAEqhCQg6mCVUJFQAREQATkYGQDIiACIiACVQjIwVTBKqEiIAIiIAJ/7SITDhEQAREQARFYScC23W7BBtyVRdXrIiACIiACTQhoiqwJdmUqAiIgArtPQA5m9+tYJRQBERCBJgT+ByhLhr6GjCNUAAAAAElFTkSuQmCC)
Answer:For mode:
Here, highest frequency is 40.
So, the modal class = 1500-2000
Mode is given by
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAN0AAAAtCAMAAAAdiJ4xAAAAAXNSR0IArs4c6QAAAKVQTFRFAAAAAAAAAAA6AABmADpmADqQAGZmAGaQAGa2OgAAOgA6OgBmOjpmOjqQOmY6OmZmOma2OpDbZgAAZgA6ZjoAZjo6ZjpmZmY6ZmaQZpC2ZpDbZra2ZrbbZrb/kDoAkDo6kGYAkGY6kLbbkNu2kNvbkNv/tmYAtmY6ttv/tv//25A625Bm27Zm27aQ29uQ29u22/+22////7Zm/9uQ/9u2//+2///b0sawXwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAADiElEQVRoQ+2aa3ebMAyGbdqsYdeEZOsuLdvalTQ0XVcu/v8/bZJsQlICEh0hZKd8aDjJi9FjybKsU6VerpcZaD0D5qfW0+anBJLWr+3nAROOVdxMJ5D0Y2v7t6T+JfeQQMINcajfE83SCSSHsp55b+JrzfAJJAOFU0rgGIFkqHgC0wWSo6GLIFTt5d1Yo/8nuqobjp7OLMb1wUV0sKN7X4cagLV2kel3H+YcXTx+TF+7UD0eSBd2MUOXB5fKhEzFNjjqxG13DXQkyWfgt6hhCgZHtmlQk+9Qt086mD62Xvq3yWPp2kdmvN5SVB4UAPGuA4kgKZtQ62dHjonOHpunJxq1zipJsWGC6wM9whfA5461KynT8+ApnAmFHocZ5Q55+Vx7F+3iY5Nudk6oyav5M+nwGLZ9ienaWV2nzj8t6afMfW7RXQeAZcJv+KFUOtf63W1x955OYfBdw456cDoTniJeHkxcBef9WriQgKQUnSxVMvpDdKl/obIQvqA78wOzCt7d1x82D04HroHFVS6QRL+9NRFFJNBh6oimOdHR1kKrDZazK2Txbo1QLXYPT4d4D/NxkZ8oFdp8CHRgXvpmSXQWEf/aO+R02JR7dl3bdBX6dem/j5vCHkjcpX207mw+xO0yPjl3OJYE7d2kI7swWgV0KOk5q9Ab6+lSH2gZ3xVgdZFpvpelbu90FJlr5z3xHa02oqP1SV618YbRW11X2y60v1PJ5K6+6Yqs4tbOJh2UOnTZUExgT88IMfauVPbRLlDInne1hyybrOKNyO2ZzrqkTJplVllXYniDeCtoVk1QbBbam/z26Rjma+9LfVKx6UJCxzeXeQWeZ7fLquyztS21n1AcezcpYAgLppp0Ivza3EOBcIpxyzeXeYVgEKFd3cgiCOwssAUCN528QjBIN2YLR6ECIS532KbHBGcSgURoWHcytIlvLvMKwSDdGS0eCWtZQYNS4BiBRGxVR0K7nnjDeIVgkI5sFg/juloV2yuFT5VOIBGbsR9hUe3wnuEVw/Nd5A4n1vam/rOg/UySB9hCJ/txRdtRYzopQiHE959J0dx+Rkk+u1KrsjfU1qAu9dQoN1FBh9bXDk+mNzf5iuAdSP/d5YUpFoAUmvV0gvZzMQj3LwVd+qfVWEyHVtZ+Xg1k2VXIOTpJ+zkeKhzbfxa0nxOAS7iSvFVAdSTm+898+xkPo4Lz21/1y2lZw7xeVAAAAABJRU5ErkJggg==)
Where,
L = Lower class limit of the modal class = 1500
h = class interval of the modal class = 500
f1 = frequency of the modal class = 40
f0 = frequency of the class preceding the modal class = 24
f2 = frequency of the class succeeding the modal class = 33
Substituting values in the formula of mode,
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ Mode = 1500 + 347.8
⇒ Mode = 1847.8
For mean:
Using assumed-mean method, as values of the data are large.
Let’s draw a table showing midpoints and frequencies.
![](data:image/png;base64,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)
Mean is given by
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ Mean = 2750 – 87.5
⇒ Mean = 2662.5
Thus, mode is 1847.8 and mean is 2662.5.
Question 4.The following distribution gives the state-wise, teacher-student ratio in higher secondary schools of India. Find the mode and mean of this data. Interpret the two measures.
![](data:image/png;base64,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)
Answer:For mode:
Here, highest frequency is 10.
So, the modal class = 30-35
Mode is given by
![](data:image/png;base64,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)
Where,
L = Lower class limit of the modal class = 30
h = class interval of the modal class = 5
f1 = frequency of the modal class = 10
f0 = frequency of the class preceding the modal class = 9
f2 = frequency of the class succeeding the modal class = 3
Substituting values in the formula of mode,
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJIAAAAeCAMAAADw17cfAAAAAXNSR0IArs4c6QAAAKVQTFRFAAAAAAAAAAA6AABmADpmADqQAGZmAGaQAGa2OgAAOgBmOjoAOjpmOjqQOmY6OmZmOmaQOma2OpDbZgAAZgA6ZjoAZjo6ZjpmZmY6ZmaQZpC2ZpDbZra2ZrbbZrb/kDoAkDo6kGYAkGY6kLbbkNu2kNv/tmYAtmY6ttv/tv//25A625Bm27Zm27aQ29uQ29u22/+22////7Zm/9uQ/9u2//+2///bJi78wAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAACW0lEQVRYR+2Wa1fbMAyG7UA3vCulzcauYd1qRgrbmjj+/z9teiWnTUjd5PAFHw7+0Pi0ivRYeiVXqeeVXAb89VliTJv3eWpISpXPSBNk8iSzVGn9fcLZJ5t4+3J71HizVqpZtFFLrS8G5tUEJH/7WutT8qWUX2n99nc0KIU4FITta4MfM7ghphnI6TkkIsPxLNnsp3IFnPlitnXFyc2eyRfj74t1J1KzvGS06kX+UCQ0dol0VvDUS2wUqfko4C48+0i/FsTii694EG3e5h67d5wl2mVfjgvGIjf80Sw6syeK5ItTMDWLefDby9IanqrZP0aqzTeqAlxj53/g8NjdHa2gW52TglA3RGEhyIoXjo07+H0kpNpeNIxkcUT+2cIzVwE7X4SzW6iQF9cbCy1yTsaCJJ+jSLD7m5/tTGvzxoQmaZZrCle/umEk4cKn7AAXWDuBhjW8M5TYe0gD+HCUPa40VsjnFcojHbdcq/LkMjBIeKSki8S+uo00ZKqoX9vCTdESR+kiscvacEYIqTZEN5KlluJA4XbOgrw7nXtkCHDh7qVetAUkVhAjyUFRLhEPtLST0TA3+MYXQGDRySToTtdxebels6IT0U0YZlIpFMAxV4kJ+EGCUO9tYlPAQwDyCpqtp+54xwWzfctZ9iJTJFwo2IDplgb7HOj+WmfzPwZMG6Ozz9HLya3aV5SjUYbe24s2Nr3dJzGrwxOnp3fjl9HhEj3FbwdJfPRDohGcXFupLO4kvh6SWb6Yb13b4IlQQUvczcmsJqf51l7faVDx3520kHgM9ybpoVT9B6YKSx9HAEEUAAAAAElFTkSuQmCC)
⇒ Mode = 30 + 0.625
⇒ Mode = 30.625
Or approximately, mode = 30.6
For mean:
Let’s solve by using direct method as values are small.
Let’s draw a table showing midpoints and frequencies.
![](data:image/png;base64,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)
Mean is given by
![](data:image/png;base64,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)
⇒ Mean = 1022.5/35
⇒ Mean = 29.2
Thus, mode is 30.6 and mean is 29.2.
Mode implies that most states have student teacher ratio of 30.6 and mean implies that on an average, student teacher ratio in most states is found to be 29.2.
Question 5.The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.
![](data:image/png;base64,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)
Find the mode of the data.
Answer:For mode:
Here, highest frequency is 18.
So, the modal class = 4000-5000
Mode is given by
![](data:image/png;base64,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)
Where,
L = Lower class limit of the modal class = 4000
h = class interval of the modal class = 1000
f1 = frequency of the modal class = 18
f0 = frequency of the class preceding the modal class = 4
f2 = frequency of the class succeeding the modal class = 9
Substituting values in the formula of mode,
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAS4AAAApCAYAAACLMsRPAAAAAXNSR0IArs4c6QAAAAlwSFlzAAAOxAAADsQBlSsOGwAAABl0RVh0U29mdHdhcmUATWljcm9zb2Z0IE9mZmljZX/tNXEAAA4+SURBVHhe7V0/bCJXGv8Gbb9bH+UxSPG5daSF1PGBm73GBY3TLL4qnpXiKggH4quIYpxqmTSh4RQ3t5HOcO6DT4pby9ECV25/vn7n3e97MwMzwwAD5p/NGymK1vPN+/O99358/9+zUqlE6lEcUBxQHHhMHHj2mAarxqo4oDigOMAcUMCl9oHigOLAo+OAAq5Ht2RPd8C5neeicnpBW/U23TfKWnCmuZ0P4uDUpOtr902K8tU6xe8bQ7SL5FLu+ZXQDaJqN3yci+xbtW1zQAGX2gkr50AxtyMOD7Kkn/BQ8tRMEN0ERiXBIou3zS7t3thAxUCmZ3VKVbtid0ngVcw9F2mdkTO1cr5t8gAUcG3y6q/B3CUQVDpUqAs6vkwTSzLBp1jMifM0UC3fpLgDWkzTuIlrzTyJ7MUl1dtF0SgPS2nznGKxCIDVsrSdz9O1eTvPplVbU3JAAdeUDFPk8+VAuXGv7cYhYTXKpD8nMVPr20laNGjxuFqHWbqtdqmdrJBpzjRS9dGcOKCAa06MVM0sjgPlckMrFvLCyGbpQ7MrXKlLqoonKdiaMrCJBZXL+Y6niL7SV1Wq16DHtubbtmpteg4o4JqeZ+qLFXCgDLWw26yKA9i0IOxIyewEdqZlGMhtFfGK9rs1KdkVd2aUDFfAt6fapQKup7qyT2xetlHcYFcelRxDvDTY6xpMXwJSWLh9a+fDichGUuvCQdC2r+lSRYyHeToxhkqyDdvbYu1rT2w5HzwdBVwPZqFqYNEccMHjOlWl7lECUo/dY+KoTtULnYzTc+qOMM7fxEta1OQQhGAMT6VVIYOdiNc64X+OpGeTGQBNQCn7DNSzZA4o4Foyw1V3s3CgS3cMHnm/EZ5tXzvbABPzjrqzNBvhG1ZRg2lxbO/SsrcDNfUmBPAitK1IZueAAq7Zeae+XBoHdNrisKnbDuVqIWEPqS3S8Xqx5vmlTVZ1FIEDCrgiMEmRLJMDt9Tp+ftjySq3nxKGYdDBeZLqRRu8bK8iQkGre0sJh3BH1euoGK5l7oiwvhRwrXoFNrx/ab86PKAL8xpeQvth2xGlUiK/P0jnadzvwqu4jZQfRNgbkkycpPJURST9vScoddHstNVEO+fI0NOsLoqw9KRFj2PT21fAtek7YMXzZ2mK4ru0W8J/wbHcN3x/4Uj53d0S7XoIAVpLnUHQ5hVq0F/qiDazs5UBl/3LZfup4c5W7uTN3H9q1ooDM3HgmZt/5Ya6jAIROyPeFpGR1EoPTWrlXy7RzPfBa6bRL/ijcVUAXBXHgIojeQJXfaF+xKkrvkoF86Zb8JRV84oDoRzI7bywKqc/a1v1X8lIaLFSuexLz8I+t6Dya77z8NMRZXSKlT20ku6vX2hGrT04N2Po3oCOO0qlzqjwk9Fv71m5fKPVBEQeJI8yeJkhMTE2uNkWiHmAVp8z+tba5tiPqwLgxhUZhLgi0aZEr0XnqG6Q1e+oKWrixkn2nTfdpDPl9ndXUBLsJF6p99E4gMod1uHBnqafMHzk6fKPmgQSbwCIBKPPkpohzqhjtUn/D87DF3uUTd7RpfXWKhaLErz8dL9OpHsjvqf31oBuL/k7/dNpz6MqorZRHsBlXtBl78g/q9Y7MvEyf2vSJvhTJlYBkEGJHGl91Pdm2bl0Jr1r1Qg5w/Yzb7poe01RKQ5QsfipdZj+h/aqXSNUAxqWkHJ4fzD6PbOwmHthfVbpaF/XLVTu+IySxgjGYp+/uX5J1fdfUlJDX40bUfz6tfVmz9R+ab2lPQxAFoifku7790cEP02sHNKez8a1dVygvJmli8te31Dq/ornCwgP5pT4/eHBs3RyeGCQozWNVpsCdFcfwmsa+dtbfrG4SVUAWu9YNs1T0ls3KvMKfzHJfNeikoNc86ZT51FxIDoHErRFP1I2TdRs16wspB5XvZOgFstot6+bZGpQ+0ql0Koc5cZ/Y5+7lTteCAt9hxZslPtc5ElPeKQxeR5+pNovyEh3kGtAZ6cgSKltDB2fr/4ToAsY5zP0iqUuo0IFV+VhqYFVogxRJYRrbg7ZNtzSJbiluShcqNrk5Jr16aQbHOkaaHPb026wPa6KyYm10MFG5qNFX8zJlJOqAPRrQ40KenSCJBPUI1lDak50yyjbMpk7iuKxcADe2lix3bEondSy6S3qtI8sHeBF9K+PDFomQIvM7EjQijpPW/37RhPOPh/67rYL9ZEsXcsR6MimC8G/AB2lPhlB10F7WWvIq5iRyDVQeRglU/tdSoxIqmhVDLpGspZblRJinVasV8UFgm28apOkgwG7nkGuGUKcZamSV1CvAoWNgnSJzB7tpwwyPJJMkDkPTaR123tYFQAnunviis+bbmKHimBDOeAFryQkr049aX0HWyyDVqeWIb0mcA4Xla6k0yesUE2ssDYdnea0NxwOkTmmasqUQCGOOSM/D+mLZbbhbDD7oLPBHhLRvSfhIpGUUtQtQqBZaxrQBSKcA8b5MLp+PtqodA+0/+BEWjnGaFUACJLUujxBwD45cUI4s/IXzbNlRpd/wTcTt9a6zFeNYywHQqUnH3jpWGoIDxK0YPfyevseG2+HgGuQXvGODtkUj8sI2EuWAUhFn5wtVZh3CJvoW6qjf31tDDLxB18tLpFW9vHgKgD+RGAGwvAZz0YX1lYQsMd5FUcFSsK+sdSLJqLvAkX5uDnQpd85Uui1TskYxYSgj/hXyF6bjk68Tsr2QgNQE3v7lEJemGnyL3UC1SWnZaF9OFP7AUksYjOjQi4AoKEtzENVjFoFoAzBclxFgtSWPedJlQumpYvIOkWmOODjgLRBwc5lEEIVukliVVGqjbB5uWEKD2EZS3Q7fxKWZt5prJNxsrv34X3O+OWnE0P2qyAdmb+jvRC6T9AeRIJQ4OI64AW+hIAKoddEDQbmSFbBywp6HRk2sd13u42QwLp3clID4/xskto8VMVpFk+XpQqCoQ8IGcFf8x5X47zpphmjolUc8IFWG6EFUA9r7dZHgnE+eZhklXEu4KX/yT4PduiD5oQ+8HkQELgSEmjYheinc0MkQuj4fGluewE6nC/GDA9wXRM0u34MkgSDCYVCBrXAOWt/T4ZQuF5F2xDPN7HYhng7u/+UnjfrgpNi7Suprny7K6y2OKs/vfMKPJrHS78/b1QVgMQRwkYMGDmdYF3bg4htgTkfO3Pmic2bTh1FxYGoHAgDLcemFatZLUuCF0nPIgXrjY3u45a6PcSqI7hKxmU5T+LLAr029sj82w/UybD3kj2ISRIvq/RVRqOajVvEdHnQ1SbR8fl6w3TnaM/ot0cvz/rt+VN+gJZhZXB9aUGwP0F/7N9jZ9cCz8uQBZiGBduHU/AydmEA9LrwuVpl8+6AshzaQClx9WGH6vV9usUddaanX9le1W6Po0NOTq5w6WeBjj2VL6Mu3kPoxlUBkNkGXWQb8F2AEML5SeURMlIbBKTy3+ZN95D5qG83jAO9Ht1tn8k9CdeazxBfLv8Wq3XOLUJw6bEQVvC9yyk3jcdXuQMGJgRqWh9QucM0EnAIlAX2Odq7tAgR9snY4Dx03joBpE7KD9O9ZbovpqF745yvM3r/1rADUtGeTPmJo7ZtH0FDqjkO0YRl7aONQdL+DUDLX9bNrQJQQhUA+wENbGe77neefhv3qALgbQ82o2B7i96Gk6oAcNhHHJUK+tOhewbqoWHNm27cvCWPMSbUP5+KPVKqbV1S5XQQRAwkhl+mNsFUMFU3E4nVTdbhLMp9ijzBb480N8Cb16aJtckmhiPi3RbKjd9icTjGwvak/FFFcOm49/YPbyM2rnKHtyQ29nksvvuN7zz8/dvQ8xD7w+eg+9wd6T1Fo/ufj25l1SEm7mJFsDQOtBAIzIU6+JZoN4j4ENdGs3Dtzb1c1IDUTdajOZt7cWUlM6SdYW2AVPDO9T62DhFUymtj+SPiF7U+69iuAq51XJVVjMlzSzRLicfVlDCNgAMiMC5pQki/I86HcxPLvSQ2II1+z7TqJuvRi22n5pxoL6sdMgBatlpGsWKtaeV/zGinP3zF1Qwd6/UqNs3q+lTAtTrer03PYY6YRJJ9vXbJntEPvMCwRDr5cP2qGBKQnOvqbxkQnWoZYe2om6zHsNfjnfevBPIQX2pkXiACXsAYTnb1hbXZUEsYiAKuJTD5MXbhJoi/gpf0ZsQtFNIL3O4KgkeV8+HcK8L6zhyAVil+8+AA1429ydqTgTIcIfUYd9X8xqyAa368fDIt2YnubPMKVwG9E/WCF0qwU7fO6iNCRfqe5fncvbOJN1mz9+8vr8kyje+0aqdmGXoxJgg2rnMU7OPgqPDiKk9mH46biAKujVjm6JN004b4xuiotzP7wEtGu3BoiD8cJvoIwikf403W88jo+HOti9osB2Sg0BUeS2Nvb2EfJWMQRrSN9JcxZWkeyvN1/l4B1zqvzpLH1q/Yug0Vz7nmfslDCO3usd5kPY+MDjckYRBGRHSka1ZaIy21xVHkwXqk67Biix+DAq7F8/jR9MBhEQZAy5aWoqt4vhLVyIercGAuq43tkMtbZ+KGusnay7Ze82f6t0jRGWIirrlY8XRhezOtwLp9pIBr3VZkReORF4NcQcVrD1Q8WVSxczz2YhQfaCEfjrMlam37DgMd+XDdsJunp56jusnaZZkbIiFgQ4T6+OBCgFMvxZp8oIBrTRZilcNwjfG+GvqIpmcJjLaORw4tDLSY2HsBi458OLeUdbQ5qpusR/GJI+jTGpL/HMdHYqGFAKOt1qqoFHCtivNr1K+sOovxXPMN0k4BQrcoIezso58eVLjt4RzNPnh1qwL5cJQrjlYZ1U3WkzcCX1qRTh5pVy/ztI8Ieg5GbcQ3K24ryKX/A6jgWGvodkPnAAAAAElFTkSuQmCC)
⇒ ![](data:image/png;base64,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)
⇒ Mode = 4000 + 608.7
⇒ Mode = 4608.7
Thus, the mode of the data is 4608.7.
Question 6.A student noted the number of cars passing through a spot on a road for 100 periods, each of 3 minutes, and summarized this in the table given below.
![](data:image/png;base64,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)
Find the mode of the data.
Answer:For mode:
Here, highest frequency is 20.
So, the modal class = 40-50
Mode is given by
![](data:image/png;base64,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)
Where,
L = Lower class limit of the modal class = 40
h = class interval of the modal class = 10
f1 = frequency of the modal class = 20
f0 = frequency of the class preceding the modal class = 12
f2 = frequency of the class succeeding the modal class = 11
Substituting values in the formula of mode,
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ Mode = 40 + 4.7
⇒ Mode = 44.7
Thus, the mode of the data is 44.7.
The following table shows the ages of the patients admitted in a hospital during a year :
Find the made and the mean of the data given above. Compare and interpret the two measures of central tendency.
Answer:
For mode:
Here, highest frequency is 23.
So, the modal class = 35-45
Mode is given by
Where,
L = Lower class limit of the modal class = 35
h = class interval of the modal class = 10
f1 = frequency of the modal class = 23
f0 = frequency of the class preceding the modal class = 21
f2 = frequency of the class succeeding the modal class = 14
Substituting values in the formula of mode,
⇒
⇒ Mode = 35 + 20/11
⇒ Mode = 36.8
For mean:
Let’s draw a table showing midpoints and frequencies.
Mean is given by
⇒ Mean = 2830/80
⇒ Mean = 35.37
Thus, mode is 36.8 and mean is 35.37.
The mode shows maximum number of patients admitted in the hospital is of age 36.8 years approximately and mean shows that on an average, number of patients admitted is of age 35.37 years.
Question 2.
The following data gives the information on the observed life times (in hours) of 225 electrical components :
Determine the modal lifetimes of the components.
Answer:
For mode:
Here, highest frequency is 61.
So, the modal class = 60-80
Mode is given by
Where,
L = Lower class limit of the modal class = 60
h = class interval of the modal class = 20
f1 = frequency of the modal class = 61
f0 = frequency of the class preceding the modal class = 52
f2 = frequency of the class succeeding the modal class = 38
Substituting values in the formula of mode,
⇒
⇒ Mode = 60 + 180/32
⇒ Mode = 60 + 5.625
⇒ Mode = 65.625
Thus, modal lifetime of the components is 65.625 years.
Question 3.
The following data gives the distribution of total monthly household expenditure of 200 families of Gummandidala village. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure.
Answer:
For mode:
Here, highest frequency is 40.
So, the modal class = 1500-2000
Mode is given by
Where,
L = Lower class limit of the modal class = 1500
h = class interval of the modal class = 500
f1 = frequency of the modal class = 40
f0 = frequency of the class preceding the modal class = 24
f2 = frequency of the class succeeding the modal class = 33
Substituting values in the formula of mode,
⇒
⇒ Mode = 1500 + 347.8
⇒ Mode = 1847.8
For mean:
Using assumed-mean method, as values of the data are large.
Let’s draw a table showing midpoints and frequencies.
Mean is given by
⇒
⇒ Mean = 2750 – 87.5
⇒ Mean = 2662.5
Thus, mode is 1847.8 and mean is 2662.5.
Question 4.
The following distribution gives the state-wise, teacher-student ratio in higher secondary schools of India. Find the mode and mean of this data. Interpret the two measures.
Answer:
For mode:
Here, highest frequency is 10.
So, the modal class = 30-35
Mode is given by
Where,
L = Lower class limit of the modal class = 30
h = class interval of the modal class = 5
f1 = frequency of the modal class = 10
f0 = frequency of the class preceding the modal class = 9
f2 = frequency of the class succeeding the modal class = 3
Substituting values in the formula of mode,
⇒
⇒ Mode = 30 + 0.625
⇒ Mode = 30.625
Or approximately, mode = 30.6
For mean:
Let’s solve by using direct method as values are small.
Let’s draw a table showing midpoints and frequencies.
Mean is given by
⇒ Mean = 1022.5/35
⇒ Mean = 29.2
Thus, mode is 30.6 and mean is 29.2.
Mode implies that most states have student teacher ratio of 30.6 and mean implies that on an average, student teacher ratio in most states is found to be 29.2.
Question 5.
The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.
Find the mode of the data.
Answer:
For mode:
Here, highest frequency is 18.
So, the modal class = 4000-5000
Mode is given by
Where,
L = Lower class limit of the modal class = 4000
h = class interval of the modal class = 1000
f1 = frequency of the modal class = 18
f0 = frequency of the class preceding the modal class = 4
f2 = frequency of the class succeeding the modal class = 9
Substituting values in the formula of mode,
⇒
⇒ Mode = 4000 + 608.7
⇒ Mode = 4608.7
Thus, the mode of the data is 4608.7.
Question 6.
A student noted the number of cars passing through a spot on a road for 100 periods, each of 3 minutes, and summarized this in the table given below.
Find the mode of the data.
Answer:
For mode:
Here, highest frequency is 20.
So, the modal class = 40-50
Mode is given by
Where,
L = Lower class limit of the modal class = 40
h = class interval of the modal class = 10
f1 = frequency of the modal class = 20
f0 = frequency of the class preceding the modal class = 12
f2 = frequency of the class succeeding the modal class = 11
Substituting values in the formula of mode,
⇒
⇒ Mode = 40 + 4.7
⇒ Mode = 44.7
Thus, the mode of the data is 44.7.
Exercise 14.3
Question 1.The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mean and mode of the data and compare them.
![](data:image/png;base64,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)
Answer:Let’s draw a table showing midpoints, frequencies and cumulative frequency.
![](data:image/png;base64,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)
For median:
We have, total frequency, N = 68
N/2 = 68/2 = 34
Observe, cf = 42 is just greater than 34.
Thus, median class = 125-145
Median is given by
![](data:image/png;base64,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)
Where,
L = Lower class limit of median class = 125
N/2 = 34
cf = cumulative frequency of the class preceding median class = 22
f = frequency of the median class = 20
h = class interval of the median class = 20
Substituting these values in the formula of median, we get
![](data:image/png;base64,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)
⇒ Median = 125 + 12
⇒ Median = 137
For mean:
Mean is given by
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ Mean = 135 + 2.06
⇒ Mean = 137.06
For mode:
Here, highest frequency is 20.
So, the modal class = 125-145
Mode is given by
![](data:image/png;base64,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)
Where,
L = Lower class limit of the modal class = 125
h = class interval of the modal class = 20
f1 = frequency of the modal class = 20
f0 = frequency of the class preceding the modal class = 13
f2 = frequency of the class succeeding the modal class = 14
Substituting values in the formula of mode,
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ Mode = 125 + 10.76
⇒ Mode = 135.76
Thus, median is 137, mean is 137.06 and mode is 135.76.
Median and mean, both gives us the average value of a data, with just the difference that mean can give us quantitative measure only but median can give us both quantitative as well as qualitative measure of a data. And that is why, mean and median have come out to be very close in this question.
Mode gives the value that appears most in a given data. Thus, the maximum monthly consumption of electricity is 135.76.
Question 2.If the median of 60 observations, given below is 28.5, find the values of x and y.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
For median:
Since, given that: Median = 28.5
We know, median class = 20-30
Median is given by
![](data:image/png;base64,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)
Where,
L = Lower class limit of median class = 20
N/2 = 60/2 = 30 [∵, given: total observation = 60]
cf = cumulative frequency of the class preceding median class = 5 + x
f = frequency of the median class = 20
h = class interval of the median class = 10
Substituting these values in the formula of median, we get
![](data:image/png;base64,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)
⇒ Median = 20 + (25 – x)/2
⇒ 28.5 = (40 + 25 – x)/2
⇒ 57 = 65 – x
⇒ x = 65 – 57 = 8
Recall, N = 45 + x + y = 60 [given]
And x = 8
⇒ 45 + 8 + y = 60
⇒ 53 + y = 60
⇒ y = 60 – 53
⇒ y = 7
Thus, x = 8 and y = 7.
Question 3.A life insurance agent found the following data about distribution of ages of 100 policy holders. Calculate the median age. [Policies are given only to persons having age 18 years onwards but less than 60 years.]
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
For median:
We have, total frequency, N = 534
N/2 = 534/2 = 267
Observe, cf = 336 is just greater than 267.
Thus, median class = 45-50
Median is given by
![](data:image/png;base64,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)
Where,
L = Lower class limit of median class = 45
N/2 = 267
cf = cumulative frequency of the class preceding median class = 244
f = frequency of the median class = 92
h = class interval of the median class = 5
Substituting these values in the formula of median, we get
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ Median = 45 + 115/92
⇒ Median = 45 + 1.25
⇒ Median = 46.25
Thus, the median is 46.25.
Question 4.The lengths of 40 leaves of a plant are measured correct to the nearest millimeter, and the data obtained is represented in the following table :
![](data:image/jpeg;base64,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)
Find the median length of the leaves. (Hint : The data needs to be converted to continuous classes for finding the median, since the formula assumes continuous classes. The classes then change to 117.5 – 126.5, 126.5 – 135.5, ….., 171.5 – 180.5.)
Answer:We’ll convert this inclusive data into exclusive data type.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAbYAAADcCAIAAACTcxOvAAAAAXNSR0IArs4c6QAALLBJREFUeF7tXb/uHbfRtb7HEIRASPIMKoRYhQonD+AiUaXKQFIbceNSTQLVMaBKlZJCD+C4cKEEKvQMSSAYgl8j30lOMB4Pd7nD/cvde7b44f7u5ZLDM+SQHJJz7vz73//+SI8QEAJCQAgMIfB/gkUICAEhIATGEJCJVNsQAkJACIwiIBOpxiEEhIAQGEXgjvki79y5I5yEgBAQAjeOQNie+ZGJ1NZNn40Do5dU06dqIJW0061qZghWalML7Rkw6hUhIARuBQGZyFvRtOopBITADAR6N5F//OMff/7zn8+omF7ZGoF//etfWJXwwedQHL78y1/+srUMyr+OgLrP8haSMpEAWps5y7HeKAdqJyjod7/73a9+9auNSmS2n3zyyR/+8Ac4SfH89Kc/3bSsU2f+97//3cYSfNhaL8ux4uCHdrU8qwvkkDKRu9WTjamckuwmwEkL+tnPfgbJ92zT0NE///nPTz/99KSI7SY2DOLHH38MrDiW4PnrX//a28IIQmJMNUww4EHO3//+97uh1HNBfZnInpHqXLY///nPX3zxxW5Cfv/997uVdd6CMGjBIMI++lk2rA8m4Oet1K1JvtREeoeUnwByXLI1YJgb+rcwouJXzB/xYLyFAjAnCitHv1SRh2uwjf76178GbmMTSa8IP1+YbO5Bv0wfNJXJEO3BFpsmZMjcfAVQMZuEiReWfijRcvOl+2r2sBx58eLFb3/729IL8ac//Ymz/uAeMQcuGzxx4MNqsrPg8fPQsCge8z/63Px6H6qBHf/qq6+YM7VjkqCg4Bkg+KYakzCobLJpnSaBzf8hsX0OH+ByGvz1b3/7G77HX6b3yX75y1/iJ/NVoaGgAzMZ38Ksx//LTPiTX5UwT+TGxHgrJBiT+UrfV1RD2ImtBweAG2jE0FDFZ/yawQevBCWaJKWmQoZexRDPSmSe1D4+W6vAvxDY/vWvlE3LqoafTMLQSvGvtbFMZWenGdNOQK/Mv+xWhgzhDV3G9zWPj9eRbw/hM9DwevfNAHiGJmGSlD3OivOqvEzfLLX5g1mcYSKBrBlBtgBDNoBOoJkGP/kmTqArJtL3Ip94dps+3YtJE4l6Wc/xJjJ0ofww4wc20y81njeRKM5rEO962bwufCPxn1kvX65/y0aIUtp9FF03kRUzPWkibfLhEWClKvo1QIKJDGj4HComMhTt9YIcgmE1Ne2D/BallNpctND+xz/+Af+Xn2mjgO+++w5/Bx/uw+Ctx48fj6XJfP/hw4dMshtM8+zZM6yY/H4XPz98+NDQePDgAT5nnIl4N3jN0Jfev3/fBCzaAwY230ggIdoAM/Fr7d/85jf8Bn/hN8BfLvqw6rStIare54YWyIHzyZMnVlA/3phKd2iCsUxsGObz8Wttr4V6Dp999pm5uV++fAmzaLqz5Tk1Avxbm0de+KNSLjKREDrMImHXtRF2lC5pWTCSP3/+/EAZyqLDLBKNhN0bFhA/2TyLMxR70BXhy8O/r169gmkOOx5hBoFkv/jFL/AlzSWsrXnTjoICAqN2/ZgMuBQBi/lbzNJN4sNzCzCvGL3gtcRQ5HUUFEE365WeRSYSrtxvv/22FQ681U+7aRW+//RhIknL8vbtW5P83bt3+Hz37t3JuuDdb775xidDD7l///7kiz7BT37yE3TLwYNcaDzoqJwwls/nn3+OF9EzMVX58ssvmeDevXv463dywos8sEJ/zps3b5pEXT0x5l9hUs8iODsGMquUyCNfkw90h0FoxglWvAI1Yf6IoReoYihiWWXzmJThjAkWmUg0XODud1Gx2zW5xnn69KlvN35Hkv2WfVjPPAQ4kYRe7HXM9LFQMiOFqYRts3LndGwfnEbKfqWmWlcJlMcv2FEoN0lDH+NC2x78ig6JL/G6dUt8wJc8+cAH9eL2LvL0pnOGNZ8HeOUtYMU9KC8YpOXsmObe+svsI+WWIXJDQWNnvyCGjRlIhj7ooQ5jYagUZo7c9UbntZ/YPMKJgj0P566ur+EMbZ6Mn8fcn/Qrh8fWR+F7G8O9KzdsEfgM+ZN5pv1qq/Q3h020Lfy1HeZZUc2gS54Y+j0xD7jXC3ddSm+JgUDA7bHv89s1tr3g87HG42dA5T4SvynFCw2SCcI6vVKpdVVc104pmMffV8Sf9AhnRQa3a7z7wrDlDqr95D97VXJ/xudgiiBuyDBsNDFBCV2Yw/rjKOvivE9uZR2PD4bGQ3bheO1O48NJisFEj61WT4cISDsdKmW2SKU2DzCR3Ce1/TiuL77++uvZtbr8i+qEPatY2ulZO62yldpc5ItsLd7S+1Mgso+zYdSLQkAIbI3AAbPIrat0vfw1T+lZp9JOz9ppla2XWWSr3EovBISAEDgEgWMW2odUVYUKASEgBFoRkIlsRUzphYAQuCEEGkwkjxnPPuCaAZVxliYPn2eyurU0pXYscNaV8OQt40z4tU4agMVn27TjdFLZa4qROTrONKh/MojWkkOeY4HXluR59neB/GQVgnbGoulM5tN/gvJY9bEyV7QzecD+WMlVeolAqc1UMDRe4ch01FVAD7ECV8nz1JlMIl9qx4eHOHXdB4U/Ku7ZoDAV7UAv/o7T9RRxvRqV2swutHHxc/Aa4hZTawZi2CLnq+ZZaidcHLxYxXk7uBLMopP6KlxLJ4pYJEZmoV2uF+yutJXN0ZLBxvlYzpwVhp/C7dQwHOH1fUJGn2IYrM8iS+34BsF7uIx1avGvfADjUl9IHyJl2VQoTPBD4Ntgl+26Lm8Ee437m7zhLQbHDlUOF/nZ0nZw+2Sax5h2AobAnDemqS/vGPH68mF0LaUlIG6VWLwUONx855d2Bd5yC9fY/VsQPrADMBMvdgac06UptZlaaPvL8KyzNevwr9k1H1qc0Jvu+a+178ElfBnP/HRYryhw3USW2mFT9mMMMfffhJgRfunqCRJoLjMmci2WDjaMIG1pEPtZw1a0EzzCbOplyP0QMZN2MIwKfiCsm0gUYbbPK4UZWuiKoK9g+5gsyB9GxBVbeD9ZzTSRpe+/jLgTGrHvt2HqEbr0oEv7PxHfc/wq/YC7nSR1Ezm4M1OayHLK4C2mMV6UmyFJE7kKS4dh6E324P5MyfewHf71nJtMZIguXLZzzvc5EyxjMk3OIsuRwzpmaeCskYztNATkb2GToNRm1hfp1wLJz03usJInQGzaSZznJYN2GJqbD6eZoD0g84HFZ8xnvi5LB1kW6G1k1PFSpKYGlq/IninRyMe4DVC7R48etQoD7ycCO3riCvxb6UrkjcBb3g9mhQJzNAzgj29IjwEvcKtIZ0+/oYlcCM2M8MgLS7y110tv71gA8CQyZYjG1vi7vnOi07JzhkiuliZEKkwK2VuycrW0kNug3ENfEkbL9k5LeozekNxInpSJRCz+GVxCSyTGuNdKALCkuFO/O087Pga1rz5DYY/NOzx9cwBtNkvHGLcHo9OT36a03Zj+VIQ5i0Ir3Aao9Rg1WIXRAY3BB5xP4lB5y3jWPD1GMttrJEuZSPDnjdGPbIQC1LwWs8dGEvaT7TztcHbgL96Q2IBrK7u+Ukbwt/NYMKOeSmEeSwffMjFQnBVNRgecZwIDTIk2DOsF1hkVbgPyDtpY5RkRKowOnLb7mzzAdvIyEt/yyfzwg8UBJIEuZrhf+ukmsyVJmUhC8/r169nFNL3IDrNw0ddU4qkTz9MO4A3uSCwUmBU+mD8LltQfXsEaEF2Fri7ERfZcCCQg9KTBMKaTSsRbXgzEn/cOOBrHcrVeUvGdVIMkIwNvjHkPASAZB1Fr7lnxJyjC6gjQYLbMlWzcZ0zA8wCWIZJ5zsIxoIIYnmuI8ngBTor2TLFtt47gjj26XXPUhilbfL30TbVz4F3GsS3Us9yuWbHNHHiXcdPWtSJEq2RV9rXUuUiWjZd3OIhzU/pIKnXSRG6qnaNM5JhRONEd7aR+M8kONJF2Dikj59nTlH0ttdDmBBVKwtJp04Al8IZgoRGo7GZOj2/stR20szOi8L5hczY4HOGEwWIcVvs2/WI7qwDFYbsMnhCutW/zETHDCfSu0P89K0na6Vk7rbKJmKEVMaUXAkLgphFoWGjfNE6qvBAQAjeJgEzkRdSeiTrOCNj4e5E6n7kal4wJf2aFjMouX+QJ1JrxdiENNjHs7ho2vnB4sLx5hu0OHJSDA/4C56470VxGO0HUMe10UqNbFkO+yGtqnxNDf7cXp5H9fQyrNs5yY5t48rrFNWHqplZj2ulGQAnyAwJaaF+hNTRFHeedPwVSOlDxF4hRdCB6OxctE7kz4OsXx4hh/uQaFgv4hhfUylgPvIW923XS9St8qhxJ2WgPRqa6dk5VuZsQViby9Gp++/YtTJ73LfKyDWOdDYZowg1c0arsoHg4QOj55Z0T3Bx79+7dpHZ2EExF5BGQicxj1WlKGLt6WDB01LCLjeBXWmjvoE46QGz0QmSKybgeO0ilIpoQkIlsguuUidEzy2A5OwcAPSVwy4TmIIRQdcuy0dsHIyATebACdigeU0gfF5IlXiAe7Q7QqQghIBN5+jYwI+o41uY6F7m14okwPMVbF6T8N0VAJnJTePfIfEbUcZzLE+/FDrphvG5z+w5O53cQQ0UsQUAmcgl6XbzbGnWcVHa3HN5qN7XBBUwyWx76gbl88ODBbqWroFUQ0AXEVWDcNpPJK26YnqD78TRJ+eBXEAHZXiojfi5hxdu2tmfLfVI7Z6vQTctbalMm8gQNItMJwx3tsVrpjvbq+s5oZ/VCleFGCOiO9kbAHp9tJuo4TzL7k3rHyy0JhEDfCGgW2bd+/iud5ik9K0na6Vk7rbJNLLRbs1N6ISAEhMDFEAg+fc0iT6BfzVN6VpK007N2WmWTL7IVMaUXAkLgphHQucibVr8qLwSEQB0BmUi1ECEgBITAKAJtJhKnRnjwuHwYK9SH2CLhVPkwBGz5IOeQOBNqoSwXOYN4wGdVBnHgW3zGaoR8yIcVnt7CiPm6UNTeJLzZ/ifVXED1bSYSVzjG6vz8+fPwEy7GMZKoPbiMhTS8MDf4gFbFp88E7CrLRc64g2xxTHFgEIcBvZWE4cOdMHzPsibvmYRa9BYAAvHDcdTRhATJF2p3gaZ5gSpINRdQ4kfWtVCZYAv8v1bVYMWQBn3SfjXDNJgVuq7vzCENci4zr4iUL9fnDMsIac0+VvJnmOg6LPXX1/q1SQaOQ3VFrCWY8uEBkSQOUk0SqAOTldrMziIpNGxNOSyAeA8/Uf2VB3M39NsytuvscSZZbsj/1atXqEVlJjtbnk5eBHsXBo/eprqdgHOsGFLNsfjPKz1rIufl7t8qWfrKPMHMZ46/0oE4Twb4g5Dt48eP+TrW4DAf3r045hu14ixxz9yq5vl9+fKlZ4udB5reWhEBqWZFMA/IKrnQtlnk2Fq4vohoXbEyPQmq6s/k4oWOOV9NfGP/sqDMupsrdEzQpiRa//dy8l8pAwryFVxfGuX4YwTy2pFq+m87pTZ3mkVmppB+fMB6HO0JEyJ8GXbGm2aX2K3G6j7QFn/22WdWFgqCQcHqe3J0wtoc9vSrr76aTHlsAkwhUd8mlI4V+HZKl2rOqOs9TCTp91q9kFgOc0c77IznOeRgH7HEhr3wjjkYxMCPiqNFyVMyiLoIeZKJz9gaJLMQEAIBgT1MZOsUkiLCEmXORY5pFO/CPmJiHzYuQCENd6R/C4Y4ubnx3Xff4cVk4qOa2vfff4+i7927d5QAKncMAanmlG1ja1/kmBeSi19z7cHT572ceRfhoC8SOY/541iunT1iQXZEhlv2g5jQF1k5tLSdn8WLVJYCmb0vFYmbzk5tJ/aN5FzRjlRzujZQarP5XKSNA1Z5fz6Rv9o2S7BHHq9gIvFTGGEmwR0rl7asfMyOeNdksKTBRIZDTpldnUmxZySom8hw3OqQDaUZlbrMKxXtSDWn03KpTQVDO8HcX+G2elaStNOzdlplUzC0VsSUXggIgZtGYI/tmpsGWJUXAkLgzAj8aKF95opIdiEgBITACgiEfRH5IlfAdOss5O3aGuEl+Us7S9Dr7V35InvTiOQRAkKgawTki+xaPRJOCAiBYxGQiTwWf5UuBIRA1wi0mchBYgZc9fOxxcorzJ7eoBJeYUVihkCoUFIvXJuYAergvXg9xyKwNTHD1sQhQf7JsIHHor1V6U0XECFEuNyGmyplbDEf8hq/JmNztUYdp+S8YxOCbKNE/w0S+Dsn+duNrTHcNrpLAPkrOfOyUCZw3Ebi3Xi2Fe2g/QTOjLoqW5HctH3ylpq1K94UunwzKxWUnUVynljaaYvHw58YzgeUHfyXMWgzFDQzRgByeA1GJwuRKWB8bW6LkRBhNaD+CwcenwGmXtkCAXQHH+Dq0aNHKCUTKQoN+/Bwdm/fvoW0FlgLHzDzePPmzRZA9Zxn1kRyfBskZqhUD/br2bNnG9U/ScwAm4iQP4iJTzEuT8ywEdrKdjkCZyRm8ItrrFfu37+/HIdz5ZA1kclaceh7+PAh/hJcDDvmqZwMbrYuMQOnmU+fPoVxtznjVYkZwPJoOCeVpWT7ILA1MUOGOKT0ik6+xbDWH3/8MZeP6E2YRbZGfd0H4W1LafJF1t2FdIqZs5LOC++LyfslVyRmCNGGINK1iRkCEUWre0vpWxFAi0q+kidmQJ6tXr8tiEPYDW3teEgkwCS2ayUrtZkNhmYL7UoswmB9ykiOTQStZo5DcLPQdCa5ayC592oHq41fYVOSAcQ29Y5XdJzvhMhEuzdr9ZZkPnnt1FVTmQolzeW67TPkxo6W7ClJ6DpMVmpztYU2ZuOwNX5nhoGvGWmZz927d/H3w4cPmYnxcmKGwVIuT8zAoOgMkK7nRAh4exFmkUkykgpxyIyF9osXL3xIVsiAf0PE/hPBO1vUFUwk0cekL+xc0/3HfTE+TYHpFxIzeERAVsPlJ57LEzNww5S9RU9XCDS1/xmSV4hDMHCOTdnGKIXznE4zRD3TKwt9kXUPSKA9gJ2ydfp2xAzhqGY4z3U9YgaM7X4hlnf4drjMOaNI6O1jYs8mZgizyLH8fdGrE4eEvYRwTPKMmsrIXGoz64ssrT7LoxEc+zUk8O7e7YgZysNJgVBBxAyZtqI0SQQqJnI2MUPSRG5NHBK2AY4iJkkqYpVkpTYVDO0EU36F2+pZSdJOz9pplU3B0FoRU3ohIARuGoEVtmtuGj9VXggIgUsjIBN5afWqckJACCxDQNw1y/DT20JACFwLAWz7+Appu+YE6tWGQM9KknZ61k6rbNquaUVM6YWAELhpBOSLvGn1q/JCQAjUEZCJVAsRAkJACIwi0GYiB7lrAudMyZqyP3fNj7ytd+6MxalkQMkKI8fW3CBrNUyE6ZwM/7dWWcqnCQGvmsG4/U25lYl979uIW4bxLn3RoVLW9jIB1RfW94DXm+5oQ746d015kTN/ZXhF7hqrFKNXDJLn2NXJyrWqdaNLzb4ghSpU3g0X4UsdzS5XL2YQqGgnqGaQZylTxFgaH/RgO24ZXnOsy4maJimqltR3h3fLmjbf0a7Ei2QFUIbdxUabyAPXaiJ9pKZA70VJWPqgDHbnH9Ke3UR6wFHrpqCcO7S5yxdRMR+hSedDeSLPyRiRZaTUpu6W0Yu/A15PnxE4U+LhaUptZhfaFH2Su4arbIvefiB3DSRB6YPMYlgOINw8WhgJJE79lKHPyhh0p67g2YUH14hVYd1gaGXoM9CHwQqvuNr9+uuv0evHQtVYvcjZkAxqeTqFZk3kZMXIpo3IjJxI4jmQuwa+EtAc+og+Xn6oE1rPa1RuvkntK8EgAjAx+B7th0zuoFHCRO8Q6s0ZIXWTOkXOm86EkmJsl2w1E4n5GowjxjHbAGF0cVCm2eQZ/1YYvjhk8YEJA1/VPJ5M6AzvYpLI+NvhQWPFXDjJUoRkJhIWsGgKpL3t50EdUR3U10TayGffT5XPJQnX2uStw5j95MmTteT/9NNPkZVvkBUG1xkhdZNyPn/+/MJTyP+A4O3XpCMg4y60NEdx13CSaHXxDprgVG512x21e+PVNKgj7wDh50lP1qSulSCJQEU7ob/Qez6mmopJGnslrJMy+yrJSvlklWaf967OKPeQV0ptrjaLLBV8IHcNVtm2OsbUD4rEv/ST8jMfeCTxDf5OsteydhVukOSQu1EyPwEnYzjB13MgAljNYPKIxbXJAAoEjN9jcz1vEYIlHXMKhbkh/jUCklDxjRba159CfvTR+iYSK26ucI/iruGSv5xFYtXsF85IYLPIwV2dsndVuEEO7Iqh6FevXmE2cYjDqx8QepBkf561ik9wi4X25b2Q/2tFCxfaWAJ43shw8usQ7powP6+chCgX2mGp4mfdq3OD5NcRlaVcWVnOlPOZK+VCBCraYXewU2WhO1TKDbPIjIR4ZfJAXiafMs3YQnv1M0bzxFv3rVKbWV9kOSx72+p/DRL7EwO7cdcMziJLKCdN5NbcIEnt1k2kd0ht1EmSct5msrp2womZJERJE+kz38L7XB7yM3N/VbavUpsKhtbDmmxCBoXb6llJ0k7P2mmVTcHQWhFTeiEgBG4agfW3a24aTlVeCAiBayEgYoZr6VO1EQJCYBkC8Bf7DOSLXAbnLm/L27ULzDMLkXZmAtfla/JFdqkWCSUEhECvCMgX2atmJJcQEAIdICAT2YESJIIQEAK9ItBmIgeJGaxqDOA+FgsHP9WvQgeCh8n0LJeXT0OMvAqhQnlZtRJf7yzEDIRiUDsMUnfx0Pm99i6Tq1TNYNPagrkB/bHskr5JrF5ooG0IpfsOmIyNcKx620wkwkOMics4tWO/JrEIl0MyV6dxkX6s0HCTgXdmX79+XcYBqutgMJ9j1TZYeqkdWn+Tn4GOVgy52iEIfYpUqiaEC4COcJ9vMmR1a+14jTq8hamM72god10riTgd/qqPDyGIotEC7VeO362V2jt98o62iTV2xc0oEPyVbWZeIUjw1icTaS3cLDSpwq3kfNSyMmKbLyKfT/Ji2bxk3swN5jCpHa9lP0LMk0dveQTq2kmqhrdIKxwhViK6SdnFSo34a6n19FsHNPOdqOzjqHVXDbLUZnYWSR2MjXJYI2NAQKyn0sBXCBIWjgYoDiLRxs1+EDoMDWgw+O7sPPd/sa6d/eVRiYZAUjVYja4bn8lC+4yFRztERxYGzI8c33777SHCJAvNmshKdtAuas4Y9OGpEySU6Rmcmc+8kOM+T8uq9MXQbYrn5cuXg5Y9mU8S5U6SEdILMPZ0gudaYqA1ouUz0Of+D1xPKPTBgweDRY/5TNF3kvHtX7x4sboDYVeUkgttGwzDQjssVLncZuIwgW8KncTJeSZ4SX2lDDEYkmRsrYHqJDka6/lsuvaE/Jn8654KqkOhgDJINqXJaKeumiYXU3KhbVXwXbKs19atejAcnPcn9NYmS21mg6ENmsjSgeL1USFIyDRBazfUoj3Bbk6aSJS1VmT5o1yTmU5IN0jFAiKT5GCQ0Y7SLJxb2OsZdpDKLGzSL1kxkVuPmoMTnRAdrtXib93wyr62wkIbG9m2pAXo2MCySXiFIGFyqgxnCne0EUDb45JnLrQi1iJUWCufybqvngAaQVfJnBBYvWhlWEfg2bNnk15IT7wRbMqkm2isdGx2o0kgt0EXmb01e6GNF9H9MYMJHTZs5cPDAAbAnhvJIhNZRnu3IQt2rUKQkEEEKkweFZrMrUKo0ERtfApihoAGj6GhJ8g+TraT/RMc5YXk4RvMQOv2EYCUh5NsvlIh/4D3H/YRE+T6hIbO8SQd6f7aYYmLTOQSodl1bSMFOiPXMB8MQUsc2P6wFXKGtmx6j1K8mxlTYD+G8/i6iVHJZ0ndd3s33xN2E0kFeQQyU8jVEYNhQrNHj5g9A62LhE5ETr06gRLEIJnz6hVcOcOkS6UsddApUHF8hO0a+kG8JyUUMel0oCfYP+amrBAqBJUEVw5ftKIr+UyKt2ICL9JgtmPaCX4fS7aibMqqrp1Kx2FTzJyF9CAnnXeBPxYFmSe67Dj+1+UKHbRQdvjRH0JaXtbqOZTaVDC0lYecLbLDZBZNYYucledyBKSd5Rj2k0OpzcMW2v2AIkmEgBAQAmMIyESqbQgBISAERhEQMYMahxAQAkLgBwSCU0u+yBM0Dnm7elaStNOzdlplky+yFTGlFwJC4KYRkC/yptWvygsBIVBHQCZSLUQICAEhMIpAm4kcDP1fIVQIFzz9/ZlSohWJGZi5L91Cq1kYNN4rr4t0CmKGkmoC9YLkavWHIzDZ2Cy4gb/HtYrYoei1AgyabLgX54Ufo2Nhpz53oPvk7RomA0BlLJlKgBmcpPfxwPF6JTBJU0goE5tXBULUcfyKogcD2+CUv49yzJv8Y2f0jwrtE+RBBSu3CLaOGr36BYaLZVjRTqWxUWvWFMea8WysMgGEZmdOU2Cvh7qEvjnYPZcUvem7pTazs0iOGK3jWwgyDGO04njCcayk5oCQHNMGAzfgzry/No9LsrgMvqJUrRAp/YURqDQ2cC5heLamiOvS+LdCxGQoYV42NmXbE0l/MgbhbCD8+/fvvQBYt6Fvjl2B3VPUhWVlTSQt95LowasHNakQM0A3sH0LodHrQmA7BMpAVp988sk333yzXYnb5QxriInk559/bkWgsyNEBWayjB946idrIuuVrBMqcLr39OlTGNl68I9ViBkYyAc0bOYrqQRVAzEDBsA6d43l08PoPaYItEiT89Qt8sLCZxrbutW3WK71uIKBSTjTcSgnXY2oF7q2dSKSoSJIR72zr1vTDXNr8kVOugsrhApjDotBz8ISYgYGUAkOxzG/JFJm6B8g5NYh7CseFgiZ978wkko+vVIuRCCJdmjSbKW+7Y15z4N4yUg/pTt7u5jz7BpWFx/uK0MKsBD/dV8vtbmImGFQuIoZbdr9mE3MUGpl0HVdWtJJrJvkn8wtnyDZCZmhdm/ywK6SMqOdwcYW4vJVOs4SYgbWcevdGwt1SDZwA/YCJnKdhbaf5RqhwsKp72xihnv37qFohhPnc/fuXfz98OGDfcNwnjB5TRGPT0HMwPUOA6Tr6QGBscaGiNzeRpcEqib8cmKGsgt4ZGYvtAfh9e4y9DKkwbyyfrquBzWNybC+iawQKmDPK8/qO5uYgR6Qt2/fWp0D+wLODDLccZN9NLvTOek2d+cv4CbvudvkZUs2NjjQw45HvohMyjoBSeBQMcOdJ/Ow3spN1HIWOckAkanFMWmsMih+ct1RrgUwgffzai5FGUgZKvfuj+B8CVHHK/nUpRqcyVMMOyzpDz8G1srS0eNx8J+5VPEuzkm41kpQVw1qNMOltZZsyqeinXpjM+iamlbSF4lk23Gx5nvrBRbaWV9kab+9bfW/+j5TITbYlJgBMvgDWWHrpqyLHWg/IzFDnWpCJmxrBComcnDNFBobW2N592FM7KSJDAcSVx/aQ9XG5L+AiVQwtGMm702lKtxWE1w7J5Z2dgZ80+IUDG1TeJW5EBACV0Ng/e2aqyGk+ggBIXDDCMhE3rDyVXUhIASmEBB3zRRC+l0ICIFbQgAbZb662q45gfK1IdCzkqSdnrXTKpu2a1oRU3ohIARuGgH5Im9a/aq8EBACdQRkItVChIAQEAKjCLSZyEHuGubtmWcsiHcguDACmUFx1uKuGWTtgIuBcSTtqdTFp/EEHfzcc4hyAh5qquZ/FAIlrdBg42GL3S4a6RYEMnXuGk/6VA9VeZRqGsptuqONfEuml/IqoeXpuWtCULnyftVkMMrBK1kZ0g/eggqvD9YlpDkq+lkpauYWnd0585dzMy8qzRIEyqZluQXuGrbVUBa7D54KrdMS8Vgonvwdx0xxviKDPDyWSbjUm8n8wDSlgrKzyAp3DQLKQw2I8FEaZh/fCQF4ABYCFDfY72rSCndNeO/LL7/0V1bn8fCsJfZG+WAm8sUXX1yAKmQjfA7JNnDXPHr0CGKEiSS7Tz4CVhN3zXYEMv5kTOCuAb2E2WXUF70Pf8+7ssmaSNr1MrTn1kGcKi27wl3j38KcH6Ocj3s2VpdDetEqhVoo/IcPH66SoTLZAgEYC9gOH0wP9g7r0MHpxXIBdiOQKblrPAkP47QyYOUZn6yJHKsbwjJiAPSOiTGXCroxYm0+fvy4AtMq3DUh/+Vzq/65a6ACzB8RovWMTfDyMptzHEsobw3RU7DM2iiQYhOBzOyQuoPcNbCPmJSYd5WxqzuPslprhE2+yNJdGCLi1f2S5Tp/zOmwhLvG51lxJra6PrvlrvEV2Tr+/oFOom6LzrdqaMoiqIYoYZ7vpV7TZDC0PQlkym0GRmg1u7OuG3TTllBqMxsv0hanYbvGOCu8i7oshng1ITWbu8YjiELHIuW1mkhke9TuTaUTQiQft1gmctP+M5h53kQarRA/+F21uols5a7Zn0DG24FQFwp/li3EUptLF9r379+3LTkOGiXBC2bjWEEjWdNkezZ3jY1d8ELicyv7QmXK3Sd3DRc1fEDOCfnx9/QnLS6//P6vmkxxUCLI38cObM3grmkikJm90C61xM2JJ0+e2E/0JHiilHPpdqmJ5P6A364isZRZQ6APbWH4bbKPyGE2d40pYLkXMugyVK0HTWMA8FMbm0XmWUd6qMWNyGAEMugLYUJqM69VuKdbCWRW5K6p84idUdFLTSSP8jx9+pSVh13zhgmjIieuJTQ8VWt7OzCyniMNE0AYVh4XmPfMm0LS/Wwl+s86VTNPEbf8FpqTnz1g2ojOsooRPBbVSm+F9UcdsUXj74+su5jbu+7J7ZpSLD8Mel+JOR04oykfI//CT/64bEg56VTyZ6/4rrFchbOsIatKXc7IXTM4i5xETwnWQoCTgMEnTyu0+naNl2cLApk6d43vm95Xvhbm2+VTalPB0PYek2aUp3BbM0Db7RVpZzeodyhIwdB2AFlFCAEhcB0Elvoir4OEaiIEhIAQKBAQMYMahRAQAkLgBwTC9rJ8kSdoHPJ29awkaadn7bTKJl9kK2JKLwSEwE0jIF/kTatflRcCQqCOgEykWogQEAJCYBSBNhNZkhn4COyewyAUiGuIdVYGpF+LmIFF+9xCfDbP3OCv9JQgDdauN2KGQERRr5G6wp4ITBIz+C4z2UGaJEduPvPtWB9Yx9DqfOnbFd0EyOzEbSYSlwtDSeGOMDaDGGXEJ2PEzYyIIYxQ5qLx8+fPy5wZxMGO4CNAgKnQ4ujxVxQxaVPCUf7Wy+aZii9JgwABPppRpkZLitO7eQRev37tVeOji9Oy2K+4coZLe7w1u8rz5s0bu2yGBowusJGpKuOlWyhfdpztil4FqOlMWi8gltw13oKEKE/+ApZX2OD9odboZP6Skw+zZiGnrBQfxCzEieItybEobUdFPytvTOZvXG1x2yxf+g2m9INxvfpeNaWaku0/GS8ySLJRS6bMQfIg4SBzVLftpNRmdhbJKlXi1tEYY6TyF/URBxtvJaeQ0+b8xynqxAwYRS35+/fvbaxDSGQ/DWRMgXfv3rWWrvRCoBWBkpjBNzxP9NSa8yHpx6KmIwANYiSaSA8ePMDn63PXZHQAFBaG51mFmAEWEAMXo+9hjQ+p8NloxWCvvf5YL0Y5G3v6J2bwkqOmGA968wZk2s9V0wwSM2D2gAUNFtdoXVh0k2FpIxIbAPvixYvK/GZGvEgIjG5VusLoqWdkVf+QweaMT3YWmanbs2fPlsR68nFDsS5A65ntwObAxaBMiEAFk1GPQIVp5mAFvacVS/L+vSoMIgdFZPSlNPsggLbHRRj04kMdkxARrRTtE17+MnLVWuJhugf7Wwkt2BovkoEBx0J5DYpdn4WsVdNN8kn6Im2hPeaLrFAClM7BjCdiNjFDWRyBY6H4EKgaym/GxNvIoTOJhgmfcXWNEVFMlqIE8xBIasc8TnTKB18ku89Y52olZvAVydNA5asPUf3WgvdFlr1vXvfPC7NuylKbS7lrTL6Ks3keRiUrziAWpdu7NGTefJeB+YK+K4gftROS6YSUTfZx3Q6TyS2jHebjO0LZX5IDcNN2TdI+jrF4j4V6HJus0W6GdlgS9WRQPSpNqc11FtrLvZAl6LOJGeoMM2B29wcb6UW+d+9eZoreITEDxcb6Gi4FNNAViXoygChNEwJGzIC3jJqpKYemxFhfczk8yR7cutAO9svMPQvCv95zxS2p8/JorzOLrJ9XGJxFBjpZKNKvMjj6ZVjTBmd2eNcPgKSsLEdyfON/wr9c0VgL8J85FT1kmlafpwSe3qOG35stt6IdNCffhv1SOnAO1+Pke2yTs0i25CbO0dkaDN0/+NwghicXmF3KPi+W2syayHL4MolppAbNWQhM78EqGbdDEZOIVIgZaPssw6Ah72YO3p9gIoMPKGOyJ8WekaBuIgdXSSdqlDMA6eqVinbqxAzhMNzkwWHWOmkiB+ebGw3w5QzJV/xcTbHUpoKhNa1djkmscFvH4J4rVdrJ4XSOVAqGdg49SUohIAQ6QWCd7ZpOKiMxhIAQEALrIiATuS6eyk0ICIFLISDumkupU5URAkJgIQI82mmPtmsW4rnH69oQ2APluWVIO3OR6/E9bdf0qBXJJASEQLcIyBfZrWokmBAQAscjIBN5vA4kgRAQAt0iIBPZrWok2OkRMO4jXxNcnZ7kAplXczLGBHYHFGcBT2dHF5wnzzXekom8hh5Vi04R4PXQFUlpxupJxpjwKwPf8uYi6XFkJVsbikxkK2JKLwTaEMCF5ZIXry2LRGqEjmbwF/+gXLsujci+uC5t4fcTWSrJfxCQiVQ7EALbIoAQYZhLbjqRRDBzmL8QCq8M9Ic45whKv21tL5e7TOTlVKoK9YcAKBkwoZtkYC95tzO8SfBswkSWvDekiykDNU6K0R9+R0okE3kk+ir7RhDgRHKQ890jgDi7Y3Hexpi/yFYE3qc8kozsqyeJgExkEiglEwKLEMBEEjsn687gSLPVSsJ84gDgizQw82WZyJnA6TUh0IRAZiI5b6GN+amtxyESjCaJZ0k3Us4ZRSDcpDiZyCa4lFgIzEdgciLZutA2+llPJcLQ4siKxMiewPrNmzdjTF7za3X1N2Uir65h1a8bBDiR3HNPmXz0BACrcqz0xbHe2hxkIlsRU3ohMB+BnS0UjgHhMBCX4Tg4iTOSk2yI8+t20TcVDO0EilW4rZ6VJO30rJ1W2RQMrRUxpRcCQuCmEdBC+6bVr8oLASFQR0DEDGohQkAICIEfEBglZhBIQkAICAEhEBDQQltNQggIASEwioBMpBqHEBACQmAUgf8HjsjPtjoXi3IAAAAASUVORK5CYII=)
For median:
We have, total frequency, N = 40
N/2 = 40/2 = 20
Observe, cf = 29 is just greater than 20.
Thus, median class = 144.5-153.5
Median is given by
![](data:image/png;base64,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)
Where,
L = Lower class limit of median class = 144.5
N/2 = 20
cf = cumulative frequency of the class preceding median class = 17
f = frequency of the median class = 12
h = class interval of the median class = 9
Substituting these values in the formula of median, we get
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ Median = 144.5 + 9/4
⇒ Median = 144.5 + 2.25
⇒ Median = 146.75
Thus, the median is 146.75 mm.
Question 5.The following table gives the distribution of the life-time of 400 neon lamps
![](data:image/png;base64,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)
Find the median life time of a lamp.
Answer:![](data:image/png;base64,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)
For median:
We have, total frequency, N = 400
N/2 = 400/2 = 200
Observe, cf = 216 is just greater than 200.
Thus, median class = 3000-3500
Median is given by
![](data:image/png;base64,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)
Where,
L = Lower class limit of median class = 3000
N/2 = 200
cf = cumulative frequency of the class preceding median class = 130
f = frequency of the median class = 86
h = class interval of the median class = 500
Substituting these values in the formula of median, we get
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ Median = 3000 + 406.98
⇒ Median = 3406.98
Thus, the median is 3406.98 hours.
Question 6.100 sumames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabet in the surnames was obtained as follows
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAASUAAACHCAIAAADfpthxAAAAAXNSR0IArs4c6QAAEa9JREFUeF7tnb2uFzcTxl/ey0AIHRGugQIRSpILoCAdFRIpUiHSUNKAUqVIpFNRJSnOBRAKCohScA0kQhS5jbw/NLyj0X7aXtv/r2eLo//ZtefxPPZ4vN6d2Uv//vvvf3SIATHQhYH/dkERiBgQA58YuIR/u3TpksgQA2KgHQO+ivxsb8e6qmQqaaRaO8ne68cBMTmIO6i2P7hRWa0n201qkiwGhgzI3jQmxEA/BmRv/bgWkhjYC3v7+++/WeP+8ccf6g8xcNwMrNjb8+fPsYTBBua333779ddfHw0v6NhOHbhqMZVcv37d+iUeYLXolDl+YhuYMatDT+LSU1FlyvTBNZSIXqbyun/74osvQGqhWHWmygR+//33ZRVXa0Hazz//vFqsoMD79+/Zd40HQm7fvl0garXKJD+MPOzNGvDs2TMGSdn4W0Af4wIRFX/79i1lfvvtt1UVsgpM6mtLsGvXrjnn/M4Sa4XX7Y1Cv/76a7tBWdDoWlXGrruWZOSwPIY0xmJFmXOiMGxG/L179+pizfGDar///vtPP/1kcI8fPwb94uKiFvocLkMce3OUW7du8fvjx4+tcZF/586dhw8fusrFiEn2RkdC6KSLY56LizF6ArJsqrO1KNOPLwD4bfOEHeP1z9yl6Me9GY5ltZhuc1mwueqrr77KrbhaHjW//PJL5qmbN2+uFt5YACwM++nTpxvljKvP8fPnn39SOE7wDMfXr1/XakBiv9hIwNpb4zLS/vrrr0ePHm0HSrI3YOhOOrVgzfDmzRtfdXzzzTfYrf2LAqy14mKAAerOmktuVxiS+3FqDZYQLjDOfNt52SiBVuHZqjucyVb98MMPLZzbAgMfPnywu4x49OTfbh1pRqOXGQaqMb+gr92Kz7mKxAGTam/m4ujaRLlezF3w3bt3Ocma2y5hQgiMiwG/xFUG6/n5OT/MIF0ItXDrL168cPlYYG6TWpfHG+MzK867Cw1mBmRuauHcclnq2RF2F8f9KqO/w7Y2ho12T548ia6ibHcq1d7MxdG1BS5ueaacvHr16lXrPwySH3FLija0nkp9V9Zws1SmLs17+fLlpF5bJCc6t+oQiYZnHs8W+fEOIrF6QTF8APOazTWtcdHObhfNVeAPbCcsFzfD3opdXAGVsYqvGH212drecE1x6y93JypOECyS0YW/dnu5UfKAyUnnVhdisu/Ozs7G3swUZFBG6vqsqFvjjvXFHwAK/7n6ZtjbpIvLHYuJtsddn82X5uiyPEwiRKNig+Fui2T+tpgj+t+5GWm2CRQ75dWrV41GwnI3wWoHXNM3LlztPqgAOs/ezMWxF+wsYPr869TbdL7xQDG/JzFEtr9cJlfbPZ7e2PKe1Xd458akzkLOb2BYwdbavlsmkJv5eNfE7z64pu/9+/etebYhXPikx3Z4Bg9P/V97lBmvssdNeeD9ZNxPt+kcFuwxaJRsKxAKeEUks/lhe5UDomMxClAsFqANnIxYc+1fUG1ya2tOzvj8smQv7/4tXbKXXIaA9vFKOxdlCz9xi9J6PP0oxh2Mk3REK1mMS93BOE+HjqCKfyv0SWwJTFpsobipascBMUlIB9X2Bzcqm7eerDiYJEoMnCADsrcT7HSpvDMGZG87o17AJ8iA7O0EO10q74wB2dvOqBfwCTIgezvBTpfKO2NA9rYz6gV8ggzI3k6w06XyzhjYZG8eEVQWm7AzpQUsBnbEQLm98TIbbznaWy3b48x3pP5n2LpZfY4smc9R5u1ZGG9z+ZFinFH5cF19qWzuPTHeabS3H/f5gJfV5vmLp4OXNpcrpkiOb0LaO59ZRwoEZeK7rCafM37StJt7v7EMAmnx1U17RzRLwTJcVLNXbYsHXhmugcKk0Wtv86a/MhpBPw3HlEaMBwo9Wqx21rDbUnhVNRsrNigb2dv4ne9EjZYb71PswN7Gr3FbcodJ0DKIsag4HFO0K8b1d9xTUCbbuVBxjlLG+eDV8KxmRGXX15MxXtjv04iIIQyH9WRBBHS5L65ds0NWn4NO5uPecpn4Q8zbM6nRnL504iAbFQFihPwVjMf1fK+E+rjrxMDM5MgXEP1bQeBdQVurV+mQ1ad/SGjPZD6Hm7en+lhKFLhibxZX5+bEGr16CpPEhlYv1iGrzw5DQgd0NUrmc7h5e7KGE5GmrOZiLrky5wbokr1Z1HbMoHjjxg3O/PPPP1nN3cPCy1l9ajW4v3Oba/k4fV0tHZET8/ZUFDspai5vT1NcFMTTkM3Rtyhx7AX5TlfsrakOOxe+kNWnStt25dwWkvlU0WuHQhby9rRuFSYXN1qK86Ys+TdbRloyXTvevXvH38uXL7dWr7X8Dll9duXcdpLMp3j8ZXV0xbw9WbiDwlvSLa/cv3HzFtMq41LZGz3Q3ZEtFOfW3ZVzo50dkvkcQ96e3B79f3mMjaRYcVMjT9Lq87eYhyg+cDuO52+2SCjI6gPLC09yDiWZz7IW45HkKg8u5T4NK8a1p/mOnvXIdHWoL+gbQdOfdBstUVnlC8qbnrx0h4w3xwExyW8H1fYHV/mCCm1M1cTARgbW3y/ZCKDqYkAMOAOyNw0GMdCPAdlbP66FJAZkbxoDYqAfA7K3flwLSQzI3jQGxEA/BmRv/bgWkhhYsTei3fSxNY0SMVCLAfm3WkxKjhhYZ6COvRELZEH1dvC2Lu+wxO+vrjdEJcTACTBQx95OgCipKAYqMJBnbwRixBBXw8e58cY0YTt26ccff7RoYsIWBtmEYgY/9344RiTwr121/CieSdZOVlBUIsTAHjCQYW8YBvFvHnmBkdhWCrGGMePad999N/hUN/FytsL0FIX8wBotXwMH5Z8+fWqSSR2LsZEfwoEIAtLSdA+GippQgYEMe8ODWZyYHU+ePCGJitvMclsIdsZsCEq3YvzARC8uLuxffpPwyyUM0o9hgcRQVtBVIsTArhlItTezK18i4qz4zZnE3EEW7xzXk/g0MrdNqm/pkKywPNuuR4jwazKQam+GOQ6nTfc842TMc18dsNws5kvNwmV1NftcsnbHQKq9jXMHZbWZ6rkp+7Bku4VjtRlzFmXhqrAY2CsGUu2NRlvuoOhq2DKxdSY/Xr9+7YqNjfPRo0csIONnq9h9iY/sIikulpPIp+LVq1f3ijU1RgwUMrCcRIVFYPwcRNwvAS9ecnjbhIwlPb/KIOuonR9/ziJmKEJs1odXBolrqJ6byiaxfDvJMSdPYmOKi3XQYrJtJ4UblVW+oMJ5qkPGm+OAmOS3g2r7g6t8QYU2pmpiYCMDGfdvG5FUXQyIAdmbxoAY6MeA7K0f10ISA7I3jQEx0I+Bz/uT/QCFJAZOjwF76sah5wGFnd9hR/s4IPZnX/7TcL/0acAXdnlpNT0PKGVO9cTANgZ0/7aNP9UWAzkMyN5y2FJZMbCNgb2wN+UX2taJqn0wDKzYG6/wjzOIHFNSSjN1O2pl2owyTfIgCp4ACAdNDJBfGFCW62UQIlgRgjEwxwznKyoy1nFStQ621Q533b/ZS/1zsTMdlG8HgVJo50G0MafDFlDyRBDiEPOvxMAIxijGYFctNmKLyaECgfOD1taFIAhrzIbNKQReuZrVv+o+qdqWfkms2xZ3OR7HBgQRMbQ1DqAYiVMcDOIVB/mFtgtMCWkp+GZ3bFgkZLnBxp4FHxlo/AB0TLWUG0xk0ix8yWeNihA+QMfdTbPHAfvpHbfK3qRq6fLnSu4EN4Ku+zdKW3qfSRfHVBoXG5bWziZsW4vGFHr8jmutGH5qXeuLk8GluG7xZjiW1cJpJE5gVuyXX35hGKXng8gSHguTWImhGWNwoyu4c+dODNVNR4FJkk1gzDdv3oy1LBa+CoSN2vipeAOCeaYMYojTW5tVck61LCEFhTvgJtkbTSdfHeuKgpXPmzdvfO1EOj3s1v6lw1gIYYHOC6PHpyUuuV1hSL5usUSXsZYLJC1fFsXkd0CsW/j4FihL2riwZ9R88eKFZ2ohRdIg6JaKuS03LHOMnvLMG1ARYo4BTBr0mCN0PHVuYW9OtS0yU+p2wE21N3NxpLVLaXcs40Pt7t27nPe4b8Y6Aj9+/OiFY0g4I+n8/JxLZlouhFr4Ckaw17K1aMFBxZjlEkQMvmJiIs+/wlS17HsLVMDh43YeP36cqHgBxIJkTBqB+O04ddYyuVzVEhlYLdYHN9XezMXhdgpc3HLPTV4lYYkNEQySH9EL0YYyhzAGevDggZ9k7GL/LDJXOya3AJMFKkSfPJAw9njLEHh+GMja3cmFWNURgb4UZxJkthpv26wKGRcoUK0AZYe4GfZW7OI2MuIrRl9tVrE3xA4SYMY8RRvbPFf97Oxs7Gpy7zwRHucgSwTKX5NTC2KBgTGEJXSqMhcvqNaoU0xsH9wMe5t0cdV3gU157vpsSjZHV6UjB73FRsUgRR9m3EIdS4l75coV/treRlTHbiOzRhKuOO6/+UarTUNVIJbbYxBx7W33BbmKjFGWVctiKatwN9w8ezMXR/JjV4apLmY1t7l240FHsjhh+YocQ8Q2XCZXqzyYthR9vivDj1p7bjQvjkU48Y1Q1mD89ludiqDOTzcI0mAbKNMHm1iDrGobx8DRVk95/hZnU3uaFB/IxP3i+PDHOmDhIZs/wxkvsQaJnNkjiR0QU+7FZ1njpy6xAeOrEXe8al1+2rMg2SjyY/ycKt5NLbR/ufHevMkHiVUgxoM+cjLo96yHY1tUywLKfaRp5Tc+m10AVfxb4UzaIZLqOCAm+e2g2v7gKv6t0MZUTQxsZCDv/m0jmKqLgRNnQPZ24gNA6ndlQPbWlW6BnTgDsrcTHwBSvysDsreudAvsxBmQvZ34AJD6XRmQvXWlW2AnzsAme/MIqFqxGCfeGVL/6Bkof7+EABPiR+11sL092r3H0E6yk3kcEJNjo4Nq+4Nb5/0SXuEfvNa4t1anhomBPWGgfD3ZIkZmT0hRM8RAIwbW7c1TUOIW/T6NkBPCcIiamcyv2KitEisGDp6B1XgcNPSYEX57dAnhGFsyom2JqkivS4PTC2eVbCfZm3EcEJOsdlBtf3Cjsiv+zeIIPW6XyK7qKUwOfsaSAmIgmYEle7M7tJje8MaNG5yxBAE6xIAYyGVg/f4tV6LKiwExMMfAkr3FlMBW/927d/y9fPmyCBUDYqCAgRX/xs1bTKvMA25PzV0Apipi4MQZWLE38oTZJzts3x9j81THJ06c1BcDBQyUv89VANa/Srv3htpJdpaOA2Ky0zuotj+4dd7n6m88QhQDh86A9icPvQfV/kNiQPZ2SL2lth46A7K3Q+9Btf+QGJC9HVJvqa2HzoDs7dB7UO0/JAZkb4fUW2rroTMgezv0HlT7D4mBFXsjwLTKx9YOiRK1VQw0Y0D+rRm1EiwGRgzI3jQoxEA/BmRv/bgWkhjIsLeYOCjmDoJE/uXq9evXLYyAH5z0bLCc8WReVozclVaSI37qmntFP29CdIiBY2Igw95Qm9gcS8NCBiESmfjH5rlEmNyrV6/8KmZzdnZm/xLFEz94T11yV9olEqLwOXmzRtuY8TQv2JtS7h3TUJMuMJBhb8TCcRhrhH6Tn+vDhw9OYkwrhIFx1Qvfvn178GV6D6K7d+8ewXUXFxfIef/+vScm4t+XL1/Gf9VbYuAIGMiwN7SNS0ryT2b5n7nC+DGz2wcPHiih5REMKamwwECGvWEYLBp9vYcHq8ss/tBWmIi1iPIse67bGEkTAy0YSLU3hj5rwrdv31ZvBH6SOz0XywrTTJozlp5Ihxg4GgZS7W2Qq4sNRuxkOwuWIN3u9HBoLtA2La9cubIdQhLEwP4wkGpvtBjnxnrS9uvZYCxeT+InfdPftjSNDnZZ/DyblsDdunVrf5hSS8TAdgZ65wtix+X8/JytyO1NT5HQLi9NO8mu13FATHZTB9X2B1f5glJMVWXEQH0GMtaT9cElUQycGAO915Od6W23bmknWevJdoOkQ6+NG6/1ZLsOlWQxsMTAZ/8mksSAGGjHgG/Cf7K3djCSLAbEQGRA+yUaD2KgHwOyt35cC0kM/A8Q8iczfxS8PAAAAABJRU5ErkJggg==)
Determine the median number of letters in the surnames. Find the mean number of letters in the surnames? Also, find the modal size of the surnames.
Answer:![](data:image/png;base64,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)
For median:
We have, total frequency, N = 100
N/2 = 100/2 = 50
Observe, cf = 76 is just greater than 50.
Thus, median class = 7-10
Median is given by
![](data:image/png;base64,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)
Where,
L = Lower class limit of median class = 7
N/2 = 50
cf = cumulative frequency of the class preceding median class = 36
f = frequency of the median class = 40
h = class interval of the median class = 3
Substituting these values in the formula of median, we get
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ Median = 7 + 1.05
⇒ Median = 8.05
For mean:
Mean is given by
![](data:image/png;base64,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)
⇒
[Refer the values from the table given above]
⇒ Mean = 8.32
For mode:
Here, highest frequency is 40.
So, the modal class = 7-10
Mode is given by
![](data:image/png;base64,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)
Where,
L = Lower class limit of the modal class = 7
h = class interval of the modal class = 3
f1 = frequency of the modal class = 40
f0 = frequency of the class preceding the modal class = 30
f2 = frequency of the class succeeding the modal class = 16
Substituting values in the formula of mode,
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ Mode = 7 + 0.88
⇒ Mode = 7.88
Thus, median is 8.05, mean is 8.32 and mode is 7.88.
Question 7.The distribution below gives the weights of 30 students of a class. Find the median weight of the students.
![](data:image/png;base64,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)
Answer:![](data:image/png;base64,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)
For median:
We have, total frequency, N = 30
N/2 = 30/2 = 15
Observe, cf = 19 is just greater than 15.
Thus, median class = 55-60
Median is given by
![](data:image/png;base64,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)
Where,
L = Lower class limit of median class = 55
N/2 = 15
cf = cumulative frequency of the class preceding median class = 13
f = frequency of the median class = 6
h = class interval of the median class = 5
Substituting these values in the formula of median, we get
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOQAAAAqCAMAAACUawd7AAAAAXNSR0IArs4c6QAAAKhQTFRFAAAAAAAAAAA6AABmADo6ADpmADqQAGZmAGa2OgAAOgBmOjoAOjpmOmY6OmaQOma2OpC2OpDbZgAAZgA6ZjoAZjo6ZjpmZmY6ZmaQZpC2ZpDbZra2ZrbbZrb/kDoAkDo6kGYAkGY6kLaQkLbbkNu2kNv/tmYAtmY6ttv/tv//25A625Bm27Zm27aQ29uQ29u229v/2/+22////7Zm/9uQ/9u2//+2///b+/fQhAAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAADkklEQVRoQ+1Z2XbaMBC1SElxm4aylS7BbZpiEghtgxf9/591FtkSeJEJqOCczAMWBzGaq9EsV/a8V3ndAUc7sJo7UnxitesJAYt9AdKpAakmysf3QnRbtRnJWFw8MMhZ7W7nE8POnZcEdbtxYq/p5dMh+G3gxdf3y0Yg9cSwB1qWYuaFoOFyczaISgxJh5l9zUAiMN4NkpDGWsl5Qj0IZHJ7fY+wWgjyyq/PJ5kn8aRf0zFtHUj5/cbIJxhvLDrDGMd17bfzuFJUxf6gOrrMmIwgabXQkwQuHWLqrBATJO9G645riFY38KQMcGIEJaRVIDnqQngkgVElCv5c0kSJfUASUAFqiSflLXZzb756XjKBAVeGMjEm4l/6LcuuB9Txwz0ZCTr3zxHNJSpZxeH2NTmuuDyWVQayxEZyRyi4OcIbi+YSFlbhGqSxPKBUEVzEyLxgb5DZnhRZhQyM/XIPMl8sHU0pZUVvx8UqbCM/Ze7V//m/INNP3Lwn6mkyt3T0awjoZPANH1CnxqIDmY4G4gN4kgOTeGof3SpmKx9HVXIqkDLoMi3JbDP2OB3NkbREl08EMvZvvDUeUhzIH4gPJ8ugt5FYx+Db1Zy43LmBBBsh7oyGaRskBl04SAlkCBMBEQ84HPPJNFAf6miXdNGwC4pL6FG2IW5jElD+GfdyDm0sD54EUPG7BwKZI+WBhkUHOAfJv5aL5hIWVsGJJ+cazxnsdDwyMO8JjOUBJBDu6YDx0ZWEgDuXXZByPYEuI/NkHUiCrjvQrV7UrSfhCBYuQ1QbDyBjH6LN8CTF75YnMSbLPFlG+hCkDo0tVuEWJB3XnSsfXh496eHNEMGicEThQR6TEeecJp7UXKLIKpyCzBJPFpTG8ulQJUr2XSQgqa6ghizx2m+SdTzo9WSatwZ1fEhziSKrcAmSMJpnSC+ft3U4QJRQBDtfYLZciE7/ty9m2B3NvAVUyaeh+pbNLc08mksUWYVLkMlndmGsnjZSU5k5j/pDg7ZOLnzLtWoDJUc1el9ldvsiv//XotWuZF+zjjvfal8ETZdNrEpsChz/brOv9kors82mxDEGq3qbfY0onk2J1QrHE2z2hRc/gQjxVU6l2JQ4xmBVb7EPerSPG2BENXfNVBbb8lardD9UcSc29II9SfDMS/MSrC33pHoB+bI9CXwAmM+j5arw/D1Jr9OrBW+Zund1EXn+r9Ot6fdYE/4B81aJ3eyLq1cAAAAASUVORK5CYII=)
⇒ ![](data:image/png;base64,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)
⇒ Median = 55 + 1.67
⇒ Median = 56.67
Thus, the median is 56.67 kg.
The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mean and mode of the data and compare them.
Answer:
Let’s draw a table showing midpoints, frequencies and cumulative frequency.
For median:
We have, total frequency, N = 68
N/2 = 68/2 = 34
Observe, cf = 42 is just greater than 34.
Thus, median class = 125-145
Median is given by
Where,
L = Lower class limit of median class = 125
N/2 = 34
cf = cumulative frequency of the class preceding median class = 22
f = frequency of the median class = 20
h = class interval of the median class = 20
Substituting these values in the formula of median, we get
⇒ Median = 125 + 12
⇒ Median = 137
For mean:
Mean is given by
⇒
⇒ Mean = 135 + 2.06
⇒ Mean = 137.06
For mode:
Here, highest frequency is 20.
So, the modal class = 125-145
Mode is given by
Where,
L = Lower class limit of the modal class = 125
h = class interval of the modal class = 20
f1 = frequency of the modal class = 20
f0 = frequency of the class preceding the modal class = 13
f2 = frequency of the class succeeding the modal class = 14
Substituting values in the formula of mode,
⇒
⇒ Mode = 125 + 10.76
⇒ Mode = 135.76
Thus, median is 137, mean is 137.06 and mode is 135.76.
Median and mean, both gives us the average value of a data, with just the difference that mean can give us quantitative measure only but median can give us both quantitative as well as qualitative measure of a data. And that is why, mean and median have come out to be very close in this question.
Mode gives the value that appears most in a given data. Thus, the maximum monthly consumption of electricity is 135.76.
Question 2.
If the median of 60 observations, given below is 28.5, find the values of x and y.
Answer:
For median:
Since, given that: Median = 28.5
We know, median class = 20-30
Median is given by
Where,
L = Lower class limit of median class = 20
N/2 = 60/2 = 30 [∵, given: total observation = 60]
cf = cumulative frequency of the class preceding median class = 5 + x
f = frequency of the median class = 20
h = class interval of the median class = 10
Substituting these values in the formula of median, we get
⇒ Median = 20 + (25 – x)/2
⇒ 28.5 = (40 + 25 – x)/2
⇒ 57 = 65 – x
⇒ x = 65 – 57 = 8
Recall, N = 45 + x + y = 60 [given]
And x = 8
⇒ 45 + 8 + y = 60
⇒ 53 + y = 60
⇒ y = 60 – 53
⇒ y = 7
Thus, x = 8 and y = 7.
Question 3.
A life insurance agent found the following data about distribution of ages of 100 policy holders. Calculate the median age. [Policies are given only to persons having age 18 years onwards but less than 60 years.]
Answer:
For median:
We have, total frequency, N = 534
N/2 = 534/2 = 267
Observe, cf = 336 is just greater than 267.
Thus, median class = 45-50
Median is given by
Where,
L = Lower class limit of median class = 45
N/2 = 267
cf = cumulative frequency of the class preceding median class = 244
f = frequency of the median class = 92
h = class interval of the median class = 5
Substituting these values in the formula of median, we get
⇒
⇒ Median = 45 + 115/92
⇒ Median = 45 + 1.25
⇒ Median = 46.25
Thus, the median is 46.25.
Question 4.
The lengths of 40 leaves of a plant are measured correct to the nearest millimeter, and the data obtained is represented in the following table :
Find the median length of the leaves. (Hint : The data needs to be converted to continuous classes for finding the median, since the formula assumes continuous classes. The classes then change to 117.5 – 126.5, 126.5 – 135.5, ….., 171.5 – 180.5.)
Answer:
We’ll convert this inclusive data into exclusive data type.
For median:
We have, total frequency, N = 40
N/2 = 40/2 = 20
Observe, cf = 29 is just greater than 20.
Thus, median class = 144.5-153.5
Median is given by
Where,
L = Lower class limit of median class = 144.5
N/2 = 20
cf = cumulative frequency of the class preceding median class = 17
f = frequency of the median class = 12
h = class interval of the median class = 9
Substituting these values in the formula of median, we get
⇒
⇒ Median = 144.5 + 9/4
⇒ Median = 144.5 + 2.25
⇒ Median = 146.75
Thus, the median is 146.75 mm.
Question 5.
The following table gives the distribution of the life-time of 400 neon lamps
Find the median life time of a lamp.
Answer:
For median:
We have, total frequency, N = 400
N/2 = 400/2 = 200
Observe, cf = 216 is just greater than 200.
Thus, median class = 3000-3500
Median is given by
Where,
L = Lower class limit of median class = 3000
N/2 = 200
cf = cumulative frequency of the class preceding median class = 130
f = frequency of the median class = 86
h = class interval of the median class = 500
Substituting these values in the formula of median, we get
⇒
⇒ Median = 3000 + 406.98
⇒ Median = 3406.98
Thus, the median is 3406.98 hours.
Question 6.
100 sumames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabet in the surnames was obtained as follows
Determine the median number of letters in the surnames. Find the mean number of letters in the surnames? Also, find the modal size of the surnames.
Answer:
For median:
We have, total frequency, N = 100
N/2 = 100/2 = 50
Observe, cf = 76 is just greater than 50.
Thus, median class = 7-10
Median is given by
Where,
L = Lower class limit of median class = 7
N/2 = 50
cf = cumulative frequency of the class preceding median class = 36
f = frequency of the median class = 40
h = class interval of the median class = 3
Substituting these values in the formula of median, we get
⇒
⇒ Median = 7 + 1.05
⇒ Median = 8.05
For mean:
Mean is given by
⇒ [Refer the values from the table given above]
⇒ Mean = 8.32
For mode:
Here, highest frequency is 40.
So, the modal class = 7-10
Mode is given by
Where,
L = Lower class limit of the modal class = 7
h = class interval of the modal class = 3
f1 = frequency of the modal class = 40
f0 = frequency of the class preceding the modal class = 30
f2 = frequency of the class succeeding the modal class = 16
Substituting values in the formula of mode,
⇒
⇒ Mode = 7 + 0.88
⇒ Mode = 7.88
Thus, median is 8.05, mean is 8.32 and mode is 7.88.
Question 7.
The distribution below gives the weights of 30 students of a class. Find the median weight of the students.
Answer:
For median:
We have, total frequency, N = 30
N/2 = 30/2 = 15
Observe, cf = 19 is just greater than 15.
Thus, median class = 55-60
Median is given by
Where,
L = Lower class limit of median class = 55
N/2 = 15
cf = cumulative frequency of the class preceding median class = 13
f = frequency of the median class = 6
h = class interval of the median class = 5
Substituting these values in the formula of median, we get
⇒
⇒ Median = 55 + 1.67
⇒ Median = 56.67
Thus, the median is 56.67 kg.
Exercise 14.4
Question 1.The following distribution gives the daily income of 50 workers of a factory.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAS8AAACPCAIAAAAk18rVAAAAAXNSR0IArs4c6QAAEfhJREFUeF7tXT2OFb0SfbxloBFCwBomQDMEEwALIBiIiJAgRpB8IQmIGCQiIiBgAQPBBIAIWAOg0QjNNnjnfQcVJfdt291t9/W9fToY9XT7p+q4jl32bZfP/f79+z+6hIAQaACB/zYgg0QQAkLg/wic49h47tw54SEEhMC6EPhDQ2PjNrms6FwaUUeSBPYtQLqEN0zkqa6rN1S9QiBEQGyUTQiBVhAQG1tpCckhBMRG2YAQaAWBWmy8efPmgwcPqCUmqe/evWtFY8khBFpFIM1G8Ap0sgv/tqpLrlxeHZ/nypUrfZraK9zkVpNKhx6qT5IvX77Yq2fPnq0Uch5JZsbENCU4vhOfGZOIJPUwSbMRYt2/fx8/GPC6dOkSYPr582fc2I6Ojl68eJEyyDW8R29i6uAmsOmnT5+aplCB8iELkvE5bkr1R69fv/7x4weL9ZIA2/39/bdv3+I5Ejx+/NiMcmZJqP6cmLBG6PvPP/9445gfkz5J6mJCa0AdZoXBzY0bNzwb8RbNc/nyZSbDvUfNzMvnQgLaFnL5pkWxVk5f7eOeR9ShJLxw71MG4lkypPn8+TP/xU2k8K60mYl9sZDKwwKUDP+ZJek22XRMkoCY+mY2bKnimIyTpComWWNjMITdunULrOPw+OjRI2shMPD69euR8e7JkyevXr2yBC9fvsSTmcfHw8NDq/H09BRt7AXAQEQX0Sa9cJCQ4Pz580zGGz4seAEHk+TTp09+xL548eLHjx+t0jkloYJzYoJR8fbt29+/fw+wnR+TPkmqYjKGjRTo7OwsgOzu3btgacRGwQQkoN+Fv7A/z42Cxp1TFBgFO4O7aIlhBNazoKcIJmzdMsFYm92NXqbitPzDhw9dE8zRgmnqSTInJmgRUJGe2vRrCiZxSephMp6N1knbpBZQJkGE00UC4O+9e/eS6SslANyYm8E/3NvbW1kFPOrj4+N47ZgYG3tHdyuYndITm/Kp8DyS1Mbk69evANw6ONzDokbP0qdgki9JWUzGsPH9+/dwSrGcQ+zgnfppWNyCHz58iHEAIwn+wuOtRLZ4sagdVMQo3UdFZD85OWEhTGOOAG8iGcdptLu7i4x0gK9du+bHSUhC/39+SQJdamPiZz0cIdFJcS1tZkwiktTFhERCHX3rJcEqDgY3JLbVGkLGvHzF+5WrOPYKyYKVob7axz2PqNO3dAQtbIWJ/rbpBV1wmfB2nyNbRBK/LMHFMBboa1+vJDUwiQAS4OmboAYm4ySpiskfC4iz0fcHgS1yWZIXXuWwkVlslTLHpoemiajTHbvstwT/yi+9onZbYhm6CBzvF3yNXkcusfLyq9AzSxKsAhTBZBwHoHhxTMZJUhWTv/sbOULOcPHXpCmLFkkhtW2nC1EjmDQiBvBpUJIx88YkGeIJQMX5f9iYKLOyC4EZEJh7bOTPOLXH4Qa7vRnaMl5FI5g0IkabY+PcbJzHKNXk8lSTltagkazBU03CpARCYJkIiI3LbHdp3SICYmOLrSKZlomA2LjMdpfWLSIgNrbYKpJpmQik2ag4Gsu0DGk9PwJpNs4vU9UaFf8iAu8y41+sBCSwE4xJtqm1YkyQ5FfjQ78RbSE98I18BO/jX9h3pzW+S05+jr9SEn6MGnye2v1m3X/LnoN5BBNm5/56JLPvUWtgkhRjpSQ1MIlLEsSFMISrYpL+atyah5/t+s/EvRFwAwcv+yKc35Hj8h9bc3uHfYcNs7NwHsE32b5MM9wilsdClhP/It4vGAGYzNi4kPgXKy2qj41VMRnsqWKXMKUHcyxcBW6wWd5MnJs18dB2SWOHno8ugcSILkEjwAZ8bJxjXosMgOzYes80uEDXeIyPcc6t4l8Qt4XHv4gYj219trBsVWOCDGajRYIDPUxEsMvGTGyKxWZNaOjD3mCTMZhmnjcGPW5W3tnZwV+8JSIYNhGrhvdgqX1czkg8BaPRFIl/Ma4LCHKtlGRorIcpkpSNf1FPkjkxgRYI5mBjJsOyTVEtM+9gNvaVS17ZRaLaQ3Lv169fSbFsgzlS4vtydk7FsSgS/yKpS06CpCQ5sR5yKupLkx91YkotOXnzJamNSSAtR5eCg0EfGsXYGDAtoF9Azpy2QZpgR7LiXwCT4jFBFP8iaY0+enDdmCAcjiFQ3+oIXnFazzUPvwxocQB8eAsk43qgf+jvfZCOoEz/KgiZgX/zF3Ii6iwz/kVyFcda35qb03j7t1RMkEjTBBboJaka/2Kl5QfhW6uuvRsmg9dUV7KR3LM+JmdN1ZZ8PMODGDw+dPKgEBiRJvdyBsmKx3qIc6BPkhqxHsax0bpgtmyRmCDj2FgDk7gkvnUC2ytuJyaJ9jcm/ZRJCRrcRDdJn8mZBUgXQsOk2LxxcjOpACGwdATExqVbgPRvBwGxsZ22kCRLR0BsXLoFSP92EBAb22kLSbJ0BMTGpVuA9G8HAbGxnbaQJEtHQGxcugVI/3YQyGUj9kPZlijcJE8abUdDSSIENgWBLDaCe2Bg1XNsNgUvySkE6iGQ9WUcvtzBh4LclrERlz6/6jZTI5g0IgbwaVCS9NiIjeF2kjHb2DxV7DRhRLnuFumNIK2EFAJNIZBmI0IP3L17NyI0ToDjhgyQ1mJzNKWkhBECG4FAmo0YAIN9/YFiiJTDJwcHB5pbbkSrS8g2EUizUQRrs+Uk1fYhkGajj/W2ffpLIyHQDgJpNmIpNSe6VDsqSRIhsKEIpNmIsDw2M9xQJSW2ENgIBPR7Y91mavBHrboKp0oXIF2EhkXiQHgi/XSRMjO9FwJTEcgaG1EJ13I2ZX1VHXCkA55qMtPyq2kiTZPLxmlNMHduNbnYmLS5Bo0kvYqT1EoJhIAQKIKA2FgERhUiBAogIDYWAFFFCIEiCIiNRWBUIUKgAAJiYwEQVYQQKILA5rGRmyr1+2eR5lchTSGQZiMP37ULe4vXqwC+m8VeShxCvnZJ1ouDat8+BNJshM44PYv7iRGPA+cNt0ADHEKOXc7b1x7SaMkIZLHRAMK45A/9hruIkdPeMioH/qUzidhWKyN0INfK534QtjJ9Id47xbHsSDPD4c9LNg7pPjMCw9gIsmF43N3dzZHy+PiYIyqG1uvXrzML2AUnk8/x+as9J9MsPUkOsj1+/NiOnvUHPuMt8vKkeF1CYEsQoK0bE7qnLiPajVfVJwDN7LBxFsIzyXkSrZ1w7I8TtzQ+WV96lIb0fQeM46250IHYEXW6ClZ9IknUNEkDMyPJGhtp9CTVCOfw/Pnzns+YedJT9U4vEuzv7/M5bpge7iiqRjI+b2G+uiV9sNRoEoEsNlLyvb09+JZGlXx1zs7OfGIbM9lnoFi+DcZAhm998eKFubWgcX6lSikENg6BAWyEbo8ePYJrapFyLl68+OHDB+ocOQsA658WkRVjnY8HiekiZoMgXhD9kfNGlGnj4YULFwJwEVoSAmwc4hJYCPQhMIyNKOXo6Ah/4TeSnOZGdiswz9Nycay7d++eraliRYdjIIrFjT1naVevXjW3FjecXtqFvEigphUCW4NAlf2NGO7AUnik5oUWxwtjJn5v7Nv93ODWteIIDC2wEUwaEYMjCpce136ZJIPHxrWLTgFARTjAjQgjMYRAEQQ2j438tAA/NvIDAF1CYGsQqOKprh2dBp0QYUIE1DRdS9h4T3Xtxi0BhEBxBDbPUy0OgQoUAo0g8NdTbUQgiSEEFogAV3c1b6zb9JomBfgKEM0b61JOpQuBIgho3lgERhUiBAogIDYWAFFFCIEiCIiNRWBUIUKgAAJrZiM+N+UH6LqEgBBIs5HhavxOX+yoiuyfEqZCQAiMQyDNRpSLzYdbttMXEQy6Y7KPiDVbd7NSEmtLdHy2m3RcA2fmQi22nW1EeIfMWjKTmTBrj5q7snX4kFdhO8mJi4Mtwriw8Z+JsVtq5b2Pf8OQNkjGBkAWvzvRtv93k/kgItZ4Fn2HhTAXb1YGHcGrvmAkFJKXT+OFt1qSEU2SCUZIYmUCNF7JWnISRCQBvBZhiE3WF4sop6J4mogYFiqpr1mn1x5YV6TAPjvxtlHKTgyTrLERqbFLGOHbMvs2n4wKQ26zKjR8dzOUdQrWHaKDNM5jH6PvhLCdiulHbOPAlktkND57USEktz4zUOXp6ekIffOzRCRBIVAfKGFndn6Bo1MC3mvXrjH7rVu3RpczPSNaH40+olmnVx2U0Nc63759g21QQtgJjBkxKErVnstG1DfivHEEB6CgHE55j4YPdglbMhgfdvQjDUNF+uevXr0ynV+/fl1KfysH6JOKvFB7N/ZH8Ur7CgQVAcVsRom6MBNhP/j8+XNYmIdiNq1REQK7oKHND2wwLhm45+cOiAVDiy1yDWAjuIGKg6Cm44QIYmpYIQEBrFXGDcvjZEMuLFzBeZuNDIGcqB30sJ5otBb5GVkXGheAv3z58s6dO/l5C6akacEjoOMDXxF9xNonsQUVTBY1gI1EqurE2juHwXypL+hGUsOhCRggi+F/1nJhfEDvw54IN+i5cFPVKFE+TB8IkwMIaFS1ujiqOzs7TABvBX3iogJYD2Mjhgu0mR/ZMGojpjjhmx4aA8bHmRIqQi1+ruiPGKhHEqgDJ22NVIRqfmkB7j17pXoRhjgiWcxbVIQaf/36VQ/kvpLpHq+l6nxlg3nWycmJxcvPL6Qv5TA2opRgzobVHfTl7MgPDg7GCWQeKYzPPDSYoJ9CjC48UyQG+ECHAo0ys2xHMi5Zmcsz6HCH4ghgymq/pUESmNZ6V5W6CuLYC4wTdt4MHHtbACuAhi1mll0+Xm9pwQjjhfEr14SPb22RyTAt8tPCCElWjo3T8YxIgsK9JdX7eYMVxXUBIU2YNUrSZyd05k1CW/af0kCGifY3FujRIkVoO18AjgDpWovi4tQloUoXAiMQGDxvHFGHsggBIZCDgNiYg5LSCIE5EBAb50BZdQiBHATExhyUlEYIzIGA2DgHyqpDCOQgIDbmoKQ0QmAOBCax0XaFFvmUfA51VYcQaBiB8WzkR6T8BGFdG3AaBlaiCYHBCIxnY9nvZQcLrgxCYOsQyGKjeaS2kQIDI76XxYWPeqrusdo6wKWQEOhFIP2dqt/vF9zDQW1zx4M+huw2eCOYNCIG8GlQksTYiOUZ7GpBHBq2Lm7wr9Zs1L0LgRoIJNh4dnaGWm0rKm/4UJcQEAJlEUiwMaBfQM6yoqg0IbBwBBJsxMwQsUksxAZu8K9+z1i40Uj9Sgik11QRJAaxcBgsA0KsN2ZMJRRUrBBoAYH0mmoLUg6VocHlsqEqFE/fCCaNiAF4G5QkPTYWNwsVKASEwEoExEYZhhBoBQGxsZWWkBxCQGyUDQiBVhAQG1tpCckhBMRG2YAQaAUBsbGVlpAcQkBslA0IgVYQmI+NPC1d+z9aaXnJ0R4C87GxPd0lkRBoCwGxsa32kDRLRiDBRpxTx4/FcdHV5L1/jn/tAEYflQPxOxCwg1E8utE68NDOT2fJvOwEVVbBv3RxfTJ/9vqS20+6bxUCyfMboS0OrEMyHqz39u1bnnaIf5kX5xz23SO9HcHHU+/4L27s4DuelMwq/D0qwnMrmbmYjMJEDvdDyinn6RXMK0kCMAVI17oMkz9WG8EIGxrJQFKR9LCHnmN4TgoZS/1Zk5YS7PXPUSBKMxFxzyp8UUZUSpK81OSRJk+iVzWBmibSNOl5I474/vTpE7xEkOTw8BBx4gAoouPgyGXc8JR223+8s7ODfyMLp6AixjQ7Tpxuhp1VDo8U9yt9D1QBKuIYajquClS3VR6alPkXgTQbr169+vHjxzdv3vB8c4xdmNqBVGRgQL+AnF2QMUKC1cGsz7uj6Dn64tChL2C/gkLQKaCDUCMKga1CgPYd9x+oMFN2p3OReeNKT5WOLnIZtVC4TQhxw1yBp0oaM4ufXq50q+QOyVNN+tsNGkl63kjyBKspwfzN+iefLJgfBjNMvEUursSQXXaRmQEb2WXYFZ9ANgh00jhqJ2gEk0bESI5AtZvDl2+YKBJHXU+nwXAPdRVOlS5AuggZJul5YwpevRcCQqAMAmJjGRxVihCYjoDYOB1DlSAEyiAgNpbBUaUIgekI/F3FmV6WShACQmAcAlzj/cPGcUUolxAQAgURkKdaEEwVJQQmIfA/JDT7bK1V1dgAAAAASUVORK5CYII=)
Convert the distribution above to a less than type cumulative frequency distribution, and draw its ogive.
Answer:Let’s make less than type cumulative frequency table:
![](data:image/png;base64,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)
Plot points (300,12), (350,26), (400, 34), (450, 40) and (500,50) on a graph.
![](data:image/jpeg;base64,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nPPTr8x/wAKeujolxLJHczrFNjzYBtKSHaFycrkcAdCOlaNFAGQPDkDW7wzXN1MpgNvGZGXMSHqFwo5OBycnge9WLjSILlrou8g+0+XvwRxsORjir9FAFGHS/s93JNBd3EcckhkeAbChY9Tyu4Z68Gr1FFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAf/9k=)
Question 2.During the medical check-up of 35 students of a class, their weights were recorded as follows :
![](data:image/png;base64,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)
Draw a less than type ogive for the given data. Hence obtain the median weight from the graph and verify the result by using the formula.
Answer:Using points (38,0), (40,3), (42,5), (44,9), (46,14), (48,28), (50, 32) and (52,35), plot a graph.
![](data:image/png;base64,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)
To find median graphically,
We have total frequency, N = 35
⇒ N/2 = 35/2 = 17.5
Plot 17.5 on the y-axis and draw a horizontal line intersecting the ogive parallel to x-axis.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAisAAAE9CAIAAABFq7VkAAAAAXNSR0IArs4c6QAAPhZJREFUeF7tnQl4FUW6hiECsoQlYQ+IaAhRlM0kOiOg0VGZETNRfLwxjDo4el0IMhhGGbYhgMoyEhnGBGQEMjDsI5KJUYkiQRJkCRAWA9nYQUNCQggQZAn3I+Xte+5Z+5zT3af79FcPD0+fPtVVf71V3X+q+jt/Nbx+/XoDJhIgARIgARLQnECA5jWyQhIgARIgARK4QYAeiOOABEiABEjANwTogXzDnbWSAAmQAAko74GKi4uHDRuWnJws4KalpeGj5RlCJwESIAESIAFVVuEyMjIiIyMFXHijrKys5fWptLQ0JyeH0EmABEiABEhAEFB4DiR8TGhoqCg9NzdX8kZRUVElJSXkTgIkQAIkQAKqeKAVK1bExMRYwg0ODhYfg4KCKisryZ0ESIAESIAEBIGGCv4eCK98UOLw4cPT09Ox5paYmCidwXnppC36I/VJnA8MDGzVqpXd7sFX58+f1+YrJ+ODZljCIQ3ScHSzmHBsNG/evGvXrvQu8gko6YEmTZoExyPVjbU4JMx74Ipw0tIbObEvOzs7OjraboaampqWLVtq81VRUVHPnj21qctJu2iGZReQBmk4egLof2zIfyibKqeS74GmTZsmRAdxcXF4/YOPPXr0yMvLE0B37NiBj6aCy8aSAAmQAAk4IaCkB7KtZuDAgXBFQo0NJQI+sjNIgARIgARIQBBQxQPFxsaKlTckHIiJEd4PEToJkAAJkAAJSARU8UDkSwIkQAIkQAIuCdADuUTEDCRAAiRAAqoQUFILp4iB0MJFREQoUpQ3hfzwww+dO3f2pgRFrqUZlhhJgzQc3Vb6GRuONLSKPBD8sBD8HkhXaePGjY7sOXfunGZfFRYWalaXk3bRDMteIA3ScHRX6n9s6Ooxqx9juArnh39VsEkkQAIkYAgC9ECG6CYaSQIkQAJ+SIAeyA87lU0iARIgAUMQoAcyRDfRSBIgARLwQwLUwtnvVP1IayjJk3qInUItHLVw/uaF9COKEJZQC0e9k3H1TpRrWvYdaejt6apDe7gK529/UrA9JEACJGAUAvRARukp2kkCJEAC/kaAHsjfepTtIQESIAGjEKAHMkpP0U4SIAES8DcC9ED+1qNsDwmQAAkYhQDV2PZ7isJfSy6kQRqOnmgcG1Zjg5FJ3XN+etPnUY1NNTbV2BIBRq2VKe9mZFK9Pcll2sNVOPccNnOTAAmQAAkoRYAeSCmSLIcESIAESMA9AvRA7vFibhIgARIgAaUI0AMpRZLlkAAJkAAJuEeAWjj7vKjwsVL4MECqBIRjg2PD0VMWY4NaOPdckEzFgmbZqIWjFo5aOGrh7I4BQysDNXuEGqsihVfhkpOTh9WntLQ0eMLi4mLxESkhIcE938jcJEACJEACfk1ASQ8EfwNWy5cvnzJlSlZWluAWFBSEM0gpKSl+TZKNIwESIAEScI+Akh4oLCwsMTER9ZeVlcHxuGcIc5MACZAACZiMgJIeCOjEKlxqauro0aMFyaqqKrEKh69MxpbNJQESUJ1AQEBAZmamVA2OcUb1WlmBQgQU7irMgcQq3OTJk7Eoh1mRWIJDysvLy8nJUchsFkMCJEACDa5crRs/459PxMS8Pftz4ID7iYmJycjIIBqjEFBLjY0ZT2hoaGxsrATC9oz01ZH6JH0MCQmxiw+CYIgdtfnKSf/RDEs4pEEajm4WVcfGmZprmwsu5RTU1l6+XnFoS3762JEJCXjZPH/+/OjoaB92CtXY7jk/BaV76+qTKDA+Pn7z5s2WheNMUVGRy+qoxqYam2psqrGdqLH3H6qesazwkcQc8e+tefs25ZePHDkSDz4svdhe6ETDrfhXTgKkunz0mTODkqtwmPGsWrVKvPWJi4sbOHBgenq6pMbGGSzKuecemZsESIAE/pfAlu+r356/f/SH+77eWY5zj0S0nzOy96zX7q45sQ2zH7ifqVOnWr4TIjn9E1DSA6G10lsfsf6G/63O6J8ILSQBEtAVAbzs+XTzqZdm7Xp/zdHdxdUtmt4U91CXpRMixg7reddtrcS7Hyy+JSUl4Q0QjumEdNV9zo1R2AMZqOU0lQRIQOcEfqy89PFnR56ZvD113eFjZbVd29084snb1ky59+UnuncKbiqMF9ID8e5nyJAhwgnpvF00TyJAD8TBQAIkoDsC3x8+N3N50fPv7ly18eSFS9f6h7We9EL43JHhTw0Kadzo/z216urq4HikBuAYZ3TXHhrkgIBaWjiPgWdnZ0dERHh8uVIXMvqkJUnSIA1Hd5biYwMve9bnndl3+Lyo8cE+QYMjg+/o1sL5ra24GZ49SRiZ1G1uehNgUAtHLRy1cCbUwl2+cm3ttyf/MHOnULjFjv/uHxmHfzhTy1269faIVtYersK57bN5AQmQgIIE5LzsUbA6FqUrAvRAuuoOGkMCJiIg/2WPiaCYrKn0QCbrcDaXBHRAwNEvex7o204H1tEE7QjQA2nHmjWRgMkJOP9lj8nhmLP59EDm7He2mgQ0JcCXPZriNk5lVGPb7yv9iDsR3tHnw4k0LLuANNyicfDYhfV5lZv2Vomret8WODiy7f13tVZ2VOunUxiZ1L2eVVZa531pVGNTjU01tn+osb/87jjChkohRBFOFEFFRdO0DAmqeF1OCmRkUnddAFfh3HPYzE0CJOCcAF/2cITIJ0APJJ8Vc5IACTgjwJc9HB/uEqAHcpcY85MACVgT4C97OCY8I0AP5Bk3XkUCZicQEBCAfRB2HfpJ7Nmzck3618mDpD17+Mses48Pee2nB5LHiblIgAT+P4GZHy5/IiZm5kdfYs+e8ye27kkfu3TFJ2LPHqIiAZkEqMa2D0o/4k6qsaUeYqdYDlYf0jhadmlldtm2A9UVh7bkp499+rlRa/81d/Xq1YMHD5b53FE8mw9pWHUK1djuda674jm181ONTTU21di6VWNf/OnqR/85LATWMeO+W7PxxMiRI/HEwQ7Ztr2mExm0TsxQ+8lp0PK5Cueew2ZuEjAtgYwtP77w7s412SdB4Lf3d1oyPqLZhfyUlBS4n6lTp3JvbNMODG8aTg/kDT1eSwKmIJBfWjNq7t65n5SePX8lMrzN3FF93ng6NHdTFvbDnj9/flJSktgbm07IFKNB0UbSAymKk4WRgH8ROFlxacayoqlLDx84WtOlXbNxv+s5/ZW77ry1JVoJlwPHEx0djWPsjS2ckH+1nq1RnQA9kOqIWQEJGJHA9esN/vnlseHTd27YVR7QsMHwX3dLG3fPw/e0l9pSV1cHxyN9xDHOGLGltNmHBKiFsw9fP9IaauGkHmKnWA5WVWlszK9alV12+uxl1PhQv6Bnozu2b9PE7q2iqhnyn4z6MYNaOPm9diOn3hQU1MJRC0ctnA+1cHtLq6Vwom9+uHd38VnngUSdxOLUiQhNJ2bo7UmrE3sUXoVLTk4eVp/S0tKEJ8SBOIOv3PONzE0CJKAhgcqaKx+sKUlM2YdfmLZr3STxv3okJ/Tu10PhbRQ0bBCrMgABJT1QcXExWrx8+fIpU6ZkZWXhGGdwgDNIpaWlOTk5BkBCE0nAfARWfnPi9b8d/HxrGZr+7K+6Qmn9m/s6mg8DW6w1ASU9UFhYWGJiIlpQVlYWFBSEg9zc3MjISNGmqKiokpISrdvH+kiABJwS2LSn4uVZuxdmHr1y9fqD/dotfLv/S4/f2riRkk8G9gAJOCKg8DgTq3CpqamjR48WVQYHB4sD+KTKykr2BAmQgE4IFJ84P2nhgXeWFB4tu9jzlsDxw7pPfD68W8fmOjGPZpiBgMIeCHMgsQqHn0mLRTkmEiABvRE4X3s1dd3hER/s2VpQ2bJZoxFP3p4yum9kT0YU1VtH+b89aqmxMRkKDQ2tqqrCvEcszQltwvDhw22hHqlP0vmQkBC74KFLhuZSm6+c9DzNsIRDGoajseKrQ5l5Fy7+dB2WP9S72eMRLZrf3BDHnnUl7xQrAlRju+c2FdTkratPosD4+PjN9QkH4syIESPw0WV1VGNTjU01tkpq7K3fV776/k4RV3TixwVFx2ssUXumWqYaW+YN6/LRZ84MSq7CxcbGrlq1Smiv4+LiBtYnKBHEGSgR8NE998jcJEACShA4VnbxnaWFExcWlJ6qvbVj84kvhE976c6wroFKlM0ySMBzAkp6IFghhNdI8EbCKPFmCMnu+pvnhvNKEiABGQSuXK1b+PnRl2bt3pRfAYXbc490+vjt/g/2bSfjUmYhAdUJKOyBVLeXFZAACcgm8MW2shfe27lywwlc8fgvOi4dHzF0YAfZVzMjCahOgB5IdcSsgAS0J5BfUo3oBsmrSyqqL/cPa43oBm8+06Nta/ux3bQ3jzWSgCCglhbOY77Z2dkREREeX67UhfoJdMjIpFKfslMsh7cjGuVnL2MLbYQWReYObZrERXdEaFGl7gvbctgpVp1CLZx7g01vAgxq4WRKazxTLnl2FfVORumUf2Ude2xMrlC7pX1xtK7O+v72bAA4uYpjQ+bY0NuTVif2cBXOPYfN3CSgTwLf7CofPn1X2pfH4HQe6NMmbVzE73/dreGN3/kwkYB+CdAD6bdvaBkJyCGA3UvHLfh++rKikxW12L0Ue5iOHtqtS7umcq5lHhLwLQF6IN/yZ+0k4DmBs+ev/P2T0lFz9+YVnm0T2HjU06FzR/WJDG/jeYm8kgS0JUAPpC1v1kYCXhMICAjIzMzcsLcWSuv/bPmx4tCWDR8MWjIhIub+Tl6XzQJIQFMC9ECa4mZlJOA9gYyMjCdiYhYsy6r96VqHuv170sfiTLMmN3lfMksgAY0JUI1tHzg1ppZcSENXNKC0npy8Kn/d2Of/e/S/Pp6zevXqwYMHa/zgkKrj2LAaG1RjuzcUdaLJk8ygGlumuFNxWS0VtzLDdPpcf/zq7N0QW8c++xpudWyDYnsLc2zI7ErFQTkZG3p70urEHq7CueewmZsEfEsAquvSkxcanNn5n1Ufwf1MnToV74R8axJrJwGPCdADeYyOF5KADwis/fbUDenBktHz589PSkrCG6CYmBg6IR/0BKtUggA9kBIUWQYJaELg2z0VhcfP59dLD6Kjo1HnkCFDhBPSpH5WQgIKE6AHUhgoiyMB9QhgAoTC1246Cccj1YLjuro69SplySSgHgFq4eyzpcLHkgtp6IHGtoPnZq480rZV438k3gl72Cl66BSrxwc6hVo499yVThQR1MLZ7Qify66EVTRDDwJF7LYACdyajSfYKbY3i/6HqN6etDqxh6tw7jls5iYBnxDYVlC1t7Q6qGXjoQ+E+MQAVkoCahCgB1KDKsskAYUJrN184w0Q3E9AAONdK8yWxfmQAD2QD+GzahKQRWBn4dldRWdbNm/ECZAsXsxkHAKuPVB5efnu3btFi1bUJ+O0jpaSgD8QEBI4uJ8mjVzfsP7QYLbBNARcD2i84lu7di2ApKen5+XlFRQUpKWlmYYPG0oCPiaQX1K9/WBV85tveppvgHzcFaxeeQKu1dg5OTnr16+fNm3amDFjXnvttbKyMvFReVvqS8zOzo6IiFCpcPnFUupqyYo0fEhj+oojOwrPPfNgx/iHOvrQDEf3DseGVadQjS3/MXsjp0tN3unTp1988cXExMSJEyci8+bNm8WBSomRSfUg/LXqXP1LXRUPMamTOK3b9v8ABfbjY7ecu3CFnaKTTvHMDJUemEYv1vUqXPv27ceNG/fUU0+NGjUKHqtjx46RkZGOvFxycvKw+iRW6oqLi8VHpISEBPd8I3OTgOkJfLa1AgyGDgqBDMH0MAjADwm49kDwInj3M3DgQLgiAMAqXNu2be2SQE6cX758+ZQpU7KyssTHoKAgnEFKSUnxQ35sEgmoRuDg0ZrvCqohv6YETjXGLNjHBFx7ILgcCBAszcR7ILtWh4WFYbEOX+EAjsfHLWP1JGBwAp/U/wYIAgT8ENXgTaH5JGCfgDMPBBH2pEmTPv3005MnT+JApEWLFoWEuPhVNsQLwg/h/6qqKrEKhwU6dgIJkIBMAsUnzmfvrl+CowROJjJmMyABZ1o4/BIIr6CPHz+OORDeA0mtw4qc85bilU98fLxVNjihESNG2L32SH2SynTk4Tp37gzhjd2qFf/KSQMVr8tJgTRD5j3lf53yz40124suDbmv3eP93A6C4H80xDAwxJ1CLZzMe/bnbC6lFNDC7dq1y2U2KQOUcuvWrbPNP3v2bLvnrXJSC0ctnKPBZh5J3qFTFyCBw7+SYxWkIRHwTISmE52k/EeoqXK6fg8EAULXrl2hLIC8TST8NNWRl8MyXWhoaGxsrG0GTKR69erlnntkbhIwJQERBCHm/k4d2jQxJQA22iwEXHsgrMWNHTsW6oPS/02nTt24PWwTPBOywFdJgmyckdTYcXFx4s0QEwmQgBMCx07Xfrm9DBn4BojjxO8JuPZAWPqAsA1raIiDINLrr79ulwumPkJ4LdLw4cMtz9idGPk9XzaQBNwlICZAj9/XsWv7Zu5ey/wkYCwCrj1QeHj4pUuXMBMyVsNoLQkYkcCpikuZ3/3ICZAR+442e0DAtQc6e/Zs06ZNZ8yYIec9kAcW8BISIAGJgNgH6LGoDrd2ak4sJOD3BFxHJkVog9zcXEsQWJRTb0mNkUktUTPso6lolFdfefWDA2jy7NfCbuvkYgmOY0OfY4NqbPe8pt6Uf1RjU41tWv3xvHWHoMB+71+F/qE/1okMWidm6O1JqxN7XK/CwaFhGiSJsC03rHPP1zE3CZCAYwJnzl2WdqIjJxIwCQFZHmjOnDkIzCOiw0kb1pkEEJtJAtoQgPu53qDBg33bhd8SqE2NrIUEfE7AtQdCkLfg4OAHH3zQ57bSABLwVwLVF65wAuSvnct2OSHg2gO1aNHi4sWLUhFnzpyBNI5MSYAEFCQA93P12vUBd7ft1b2lgsWyKBLQOQHXHqh///5ow6ZNmyorK+fNm4cwB1FRUTpvFc0jAQMRuHDpGidABuovmqogAddqbFQG9cHXX3996NAhLMf17t3bZWxsb+yjGtuSHhW3ZqCxKrsM/yJ6tpowrLv8e4djQ59jg2ps+WP4Rk6daPIkM6jGphrbVGrs2p+uxY7/DiLsnUVVtg03dDRoncigdWKG3p60OrHH4SqcUGDbTU5iY7vn/ZibBExPAOtvWIWLDG9zT1gb08MgANMRcP0eCEj27dsHNbZgs2PHjrZt25qOExtMAioQgPqAb4BU4MoiDUPAoQfCTgoIbo00YMAARCadMGGC+PjYY49t377dMO2joSSgYwJwP9Bh974tMOqOIB2bSdNIQC0CrudAZWVllvLrZs2aVVVVqWUOyyUBMxEQE6AnftHOTI1mW0ng/wjI0sKNGTOmefPm2Py0trYWq3CPPvpofHy8ShSphbMES72TH9PI2Fqx+MtTd3Zr8e4fQj24mzg29Dk2qIVzbzDLUUScPn0aO85hk7rU1FRslirnEo/zUAtHLZxJtHDDpu2ABO7bPRWeibUQH8sRKM8K9OwqmiHzhvX4kejfF7pehYNDa9++PSY9iYmJ2B0V74Hcc3HMTQIkYEMgPfeH01U/3Xlry0F9qOvh+DAvAdceyFaWTTW2eccLW64QAUrgFALJYoxNwLUHsmof1djG7nBarwMC2Icbu3GHdQ2M7kcNgg76gyb4joBrDyTJsqnG9l03sWa/IsAJkF91JxvjBQHXHsi2cKqxvQDOS81OYP32smOna2/r3OKRiPZmZ8H2m56AazX27t27165dK4EqLS0Vv0tVCR3V2JZgqbj1Pxpvzis6WnYpIbbrr/oHe3MTcWzoc2xQje3eqHYp9YMUe7NFKioqcnmJNxmoxpYp7vRMO+vZVVTcKtUpX+WdhgL7DzN2WhbITjEDDW+ein58raxVOGxShx0ZRIJ/gzrOkZdLTk4eVp8Q0lTkwYE4g6/c843MTQJ+R4BvgPyuS9kgrwi49kD4+9dyFe7w4cOrV6+2W6fwTPjt6pQpU7KysvARCQc4g4TlO2z47ZWxvJgEjEwgO7+i+MT5kHZNh/yyk5HbQdtJQDECzjyQ+CUQ4pBid1RpmwYsyDmqHKo5/GoV3+IgKOhGpMXc3NzIyEiRHzurlpSUKGY4CyIBoxHgBMhoPUZ7VSfgeg5kZQKiw73yyivO7RJzHfgh/I9tVUVm+CR4MtUbxApIQJcEth6oPnC0pkPQzbEDOuvSQBpFAj4g4FoLh5lQQUFBbGysfOsSEhIQxQcvjcTbIGjn8D8iKWAhTkySrNKR+iSdDAkJsVtX586dof/R5isnjaUZlnBIQyaND7+4eODYhafvD3y4dzOr0eUZQw5RmU8kz/B6dhVMohZOZr/8nM2lygLit3Xr1iEbRHHv1CccOLlq4sSJIj/S4sWLEc9UOsZHl9VRC6eU7MouasqufCK72rL/DCRwcUnb2SmCgGfj0NB7lrt89Jkzg+tVOOwPlJeXB3+VmZmJzYGwqrZ06VJHXm7SpElYppMmTD169BDXIiGcDz665x6ZmwT8ggDfAPlFN7IRyhNw7YFQ58WLF8vLy+FCnn/++d69ezuKiSDW2SB+kwTZWIiDEkF8hBJBiLmZSMBUBHYcrMovqW7VvNHQB+wvL5uKBhtLApYEXHsg4Tb++Mc/3n333dimwQk+TH2E8Fok8foHL34sP5I+CZiNgJgAxfyyXaObGpqt7WwvCTgn4NoD4Xq8y4EXweZAOA4PDx86dCixkgAJyCGwq/hsXuHZwGaNuBW3HFzMYzYCsjyQJRRMg/r37282TGwvCXhGQHoDdHNjt+81z2rkVSRgIAKu1dgaN4aRSS2BM/qkoWl8f/TCpMWl8D0fj7mzRdOblL2VODb0OTaoxnZvnOtNAkg1NtXYjsak4QKkTl50ACLsRZ8fMaf+WHHJNdXYentce2+Pw5UBbMowZswYeDMczJs3zz23xtwkYHoCBUdqcvefgfqAEjjTjwUCcEjA2do0VNeQVh88eBDx3BBoR0rwSSRKAiTgnID0Bqh1i8ZkRQIkYJeAQw8EucGzzz6LOKT4SSlc0XqLtHXrVtIkARJwQqDw+PlNeyogvuYEiOOEBJwQcDYHwkao06ZNe+655/BjUhxISciymUiABBwRkCZAbVs1ISUSIAFHBORq4RCfFOF5sFWd2lJsauEsu4p6JyPSOPxj7Zj5N/bK+ujNO9u3VmsJjmNDn2ODWjj33K0cMQMiiiLWNUKOjhgxAjEOnEcmlVOgkzzUwlELZ3Qt3KwVRZDA/X1tqfdRUA2t/qIWzsuHoRkud/0rOcx+vv3227feegurcCkpKV26dPn3v//tnpdjbhIwDYGjP17M2nEazR06iFHgTNPrbKinBFx7ICy+wetIi2/33nvvqVM34lwxkQAJ2BIQb4CwDzd24yYfEiAB5wRcvwfCHGj69OkzZ84UYUmx6dzJkycnTJigElm8B8o80G5PabVK5bNYElCVwPXrN4pfOPaebh3+3050NTU1LVu2tFu1Z19h4y5Hrxw8K9Czq2iGZZ86oaHqqDNw4XKWGlNTU1988UW8B0LCwa5du+Rc5VkevgfieyDjvgd6f8WNIAiPjsmxbYLiL0UMFyHC5G/FPHseqnQV3ujjlzaicDzVpWNxBm/94Uqlqm0z4CtsQyrtPuqNka5X4eBdIb9+4403evXqhc1+MBlSWw5nYH9O001M4MfKS1/uOGNiAGy6YQjgBzbbt2+HuYgzgP+tdm7Dcz43N1c0BmtglZWV6m3t5noVTmOoVGNbAqfi1kA0Fn5xKnNbxYN9g77dW/XJ5D5q3zgcG/ocG1qqsd955x3MB4YMGSKhwE7WiFmDWYvL4YddQ6dMmbJkyRL4G2lXa3EV3BIiEEB6hmOx7yh2vl61apX4FleFhYWJ85BGSwf4CntkDx48GO4qOTlZ7I4dFxeHwuHGJk+ejI8oRxT7f8mbCZQa13IVjqtwRlyFKz/7E9bf8K/oeA1X4UQPKr7waGhtuhpPy88++6xhw4b4XxRu9dF5jfiNDZbRsBxnN5u0EGe1BCctvtkeSAt6+AqFi2JF+agIJ+1WJGsVzqU7ZQYSMDkBIYEbeHebsK6BJkfB5itFYPqyokfH5Dr5N+ebNn1jZz7xREz/p/6KfzjAR5x0dAkKlGzDHtaYpiDwjTiTkJCAWRES5iv4iIlRQUEBDqQlOPGtNBNy0kbMjRBQVORHRDfMqMQUSqz4WSV6IKVGC8sxL4Gqmiuf1HsgboRq3kHgo5a3u/3+fk/OzF83Fv9wgI/yDQkKCsLbfZEfv/XERthIWGHDR/zqBv4JK2xwHviIVTX4KnyLVTU55SObKA0Ji3JYiMMBVvawTOetB4Ifsy1Fjk3MQwL+SgAToLq664P6tO3Ztbm/tpHt0p7AuN/1/Gr2AJf/3nm5V8OGDfAPB84zo0CZrYDbEFMZuCJxCdwV/sdJqxLatm0rTmLyJA6Cg4PFSyCrhDdAtpe7PQcKDw8fOnSozGYwGwn4PYGai1fXbr4xAWIYbL/vax02ENKDmJiYjPqEA3xUykgsxKEooYJDyVhGw6qarQtBBrgcfDVnzhwxYcL6Hv4Xq3BIOMakRRxLi36SkdTC2e8vCo0suZCGExorNpat2VQWFd5qXHx3ke3pKXuphVPqOSizHP0MUS21cJL7EXI4q48y0fk4mxyFBn6dBDEDRBEQ/2EtT84lHuehFo5aOANp4S5euvrbcd9BAre7+Kyk/qIWjlo4jx+Abl2IdS1JCCfJ4XDSrUJ8m1nWKhymV7W1tRB633333StXrsTioI/dJqsnAX0QgADh4k/X7r0jqF+P1vqwiFaYiABmBZY/BkLL8VHOj4H0w8i1B4L0oGnTpggEJyQN2Dh1x44dThqAJT8I+0QGvJuSVgOlk/ppPC0hAW8IXL5aJ+1E5005vJYETEvAtQeyRXPp0iVHvOBmxPsrKUFBITR5UPuZljIb7pcE4H4gQ7inZ5uI8DZ+2UA2igTUJuDaA2HqA5eDkNiYDIloDULwYDfBzUgCc7VNZ/kk4EMCkF//PAHiPkA+7AZWbXACrj0QGvjyyy9jR4ZFixatWLGid+/eQmwnM+E3sWIhDr9pknkJs5GA/gnA/eCHqH1CW9/X68bvJJhIgAQ8IKC8GhvvfqBcsF1zgxNCjCC7MVaP1CfJ+pAQ+5tLdu7cGZpLu41U/CsnKBWvy0mBNEPmmNa+Uyb868zZC3WvDG7Vt/vNkpHCjJELyj985cZmWpZJcQs5NvQ5NrRUY8skoOtsTqR4p0+fxr4Rtsn5/kCQbtuNduckOJ2lDVRjU42tfzU2JkBQYP9x7h4rU0XoTKqxqcb2rcTZQLU7W4U7ceIE3vpYJexWt3btWg+cKuI08BWRB9x4iQ4JUAKnw06hSUYk4MwDYecJ/LhJSoMGDUKcVMgQnETlwVIb9oEQ734Q1Q5JUmMjVp2IecdEAoYmsLmgFpvRhd8S+EDfdoZuCI0nAZ8TkKVEwJZH+JUP3Al+DwSH5GSPVCkeKg6QWYREFclqEySft5wGkIBnBL7ZW4sLGQXOM3q8igQsCbjwQOXl5dCw/f3vf8fUB+IC27hypEkC5iEQEBAwJXnZ6eproV1aPHxPe4ThwhnzNJ8tJQHFCTi7f6BqGzt2LKocN25cjx49xO+BkMQWRkwkYDYC8xatSRrzfMWhLUMHhUhRIM0Gge0lAQUJOFNjY/Htr3/9q21ldvb6Vs6i7OzsiIgI5crzsCT9hNqFitfDNih3GWmA5efbKz7+/BTcT3762HF//vOMGTNWr16NYIm2mBkbW7mhJ7ck/QxRqrHl9pnIpzfdHtXYVGPrTY2NANjTlxVCfo1/f/t3yciRI3HjQHFjayfV2JZMBA27SfGvCgsLNavLifFOzNDbk1Yn9nAV2z2HzdxmI4BtF15P3rNhZ/nNjQPejg8LbXoQL0ThfqZOnargbmBmo8r2koAgQA/EkUACDgks//rE2/O/P1lR27dH63mJ/S6X7cBmkfPnz09KSlJ8S0p2AwmYkAA9kAk7nU12TaCy5spfFh1Y/MVRZI17uOv7r999S4dmYjvk6OhonMRGLMIJuS6LOUiABBwQoAfi0CABawK5+8786aPi776vDGrZOGn4HS8PuVXkqKurs9wQDMc4Q3wkQAIeE1A+MqnHpogLqYWzBKgfhY95JHlLv/7h05xy9EJUeKtXn+gS3LKx1ZB22SnUwnn5EPDgcped4kGZHlwCM6iFc4+bThQRkhnUwlEL5yst3LGyi2NS9wnN2+LMEo/NYGRSRibV23NVt/ZwFc49h83c/krgq7zTryfn7ymp7tKu2azX7np6UAd/bSnbRQL6IUAPpJ++oCU+IzD3k9JZK4p/ulL3q4j28xL79g9r4zNTWDEJmIkAPZCZeptttSFQeOz8iA/2ZGz5Ed8kPHX7n4f1bHbzTeREAiSgDQF6IG04sxY9EkCgnZF/21N84nxY18AP/9j3yYG+D4CkR0y0iQRUI0APpBpaFqxjArU/XZuxvAhx3mBjzP2dUt/sG94tUMf20jQS8E8CVGPb71f9iDvNI4N2eYcp1Sl7D53/KPPkD2d+QqCdV4Z0eahfkMuqLTO4NINqbLd4KpLZZacoUovLQqjGdonIOoPeVHpUY1ON7bEMWk4QzGVfHRd6awivDxwq9yCcpcsgmFRjU42tt+eqbu3hKpzbPpsXGJTAmerLVoF2urS72aBtodkk4B8E6IH8ox/ZChcEEGjn9Q/ybQPtEBwJkIAPCdAD+RA+q9aIwMeZR5PSDlbVXPnlXcHz3uw3oHdbjSpmNSRAAk4J0ANxgPgzgeOna/+SdmjVNyfQyBd/c+vUP9zZtnUTf24w20YChiJALZz97tKPtIZaOKmH3O2UjflVCzJPItJB57Y3vzqkS5/bldFbuzSDWjjtn4EuO0Ubk6iFc5uz3jQS1MJRC6eIFg7baQvN27S077HNthyZnMwdpqmF4xD1YIjq7UmrE3uUX4WbNGlSQkKC5AnT0tKG1afk5GS33SMvIAH3CVgF2vnj0FsYaMd9iryCBLQgoLAHgu+JjIyUDC8uLs7Kylpen0pLS3NycrRoE+swMYF1OT8w0I6J+59NNxgBhT1QSkpKr169JAa5ubmSQ4qKiiopKTEYHpprHAIi0E7Kp4dgMgPtGKffaKmpCSjsgWxZBgcHi5NBQUGVlZWmhs3Gq0YAgXZeT96zYWc5Au28HR826ulQ1apiwSRAAooRUN0DKWYpCyIBBwSWf30iacmhkxW1fXu0npfY79FIbi7HsUICxiCgvBob737mzJmD5TgAgAwB857ExERxjP+HDx9uC+ZIfZLOh4SE2IUHXTLEjtp85aT3aIYlHN/SqL5QtzKnZu+RyzDpsX7NY+9rYdtxilvocmyMXFD+4SvtrbJpbwbvFEFAcfJOCkR1PXv2NMazXydWKq7JKyoqGjFihCh28+bN8fHx4hgn8dFldVRjU+oqU+qas7fimcnboLfG/19tO+5BjNFz5855cBXV2ByiMoeoy8cdMyi8CgfV9eTJk6uqqnCQnp4+cOBAKBGEGhtKBHzUid+lGUYnYBVo5747Wxu9RbSfBExIQGEPJITXIsXGxgIoluDER7vrbyYkziZ7SQCBdv40bz8D7XiJkZeTgB4IKOyB9NAk2uB/BAICAjIzM9Gur/JOv56cvyHri68/GDTrtbuGPdLV/xrLFpGAeQjQA5mnrw3c0oyMjJiYmGmpX85aUXyyMGdP+ti1a9P7h7UxcJNoOgmQQIMGymvhvKSanZ0dERHhZSHeX66fQIeMTIre3Haw+v15n6xf/Obtv3zx8NbFq1evHjx4sPe97FkJLscGI5N6Btabq1x2ijeFy7+WkUnls/o5p97EGNTCUWhkSaD01PnJiw+IGKP9f/UyRi2kLraD1jNVm2dXUQvHIUotnFKOg6twbvtsXqANgdrL1xZkHHn1/Xxsb4rQolHtS/O/WQj3M3XqVPFOiIkESMDoBOiBjN6D/ml/xpYfX3h355rsk2jeb+/v9FxE2Yzxw+fPn5+UlCTeCdEJ+WfHs1UmI0APZLIO131z80trRs3dO/eT0rPnr0SGt5k7qs8bT4c++8xTcDzR0dEwf8iQIcIJ6b4pNJAESMAFAXogDhG9EDhZcWnGsqKpSw8fOFrTpV2zcb/rOf2Vu+68tSXsq6urg+ORDMUxzujFbtpBAiTgKQF6IE/J8TrlCFy/3uCfXx4bPn3nhl3lAQ0bDP91t7Rx9zx8j3VoNeUqZEkkQAK6IEA1tv1u0I+40+/V2Bvzq1Zll50+eyO66EP9gp6N7ti+TRO7vWKUTqEaW/tnm37GBiOTutf7SonqlCqHamzzSF33lla/NW+fUFq/+eHe3cVn0XYnCmmXMmi7g9AzybU3Zjw6JkcDvbhRaOikU3xuhlJPSD8rh6tw7jls5laEQGXNlQ/WlCSm7NtdXN2udZPE/+qRnNC7Xw9GF1WELgshAcMQoAcyTFf5jaErvznx+t8Ofr61DC169lddl4yP+M19Hf2mdWwICZCAfAL0QPJZMae3BDbtqXh51u6FmUevXL3+YL92C9/u/9LjtzZuxEHoLVheTwIGJcCb36AdZzCzi0+cn7TwwDtLCo+WXex5S+D4Yd0nPh/erWNzgzWD5pIACShKgFo4+zj1I60xuhbuwqVrK7PLMrdWAHRgs5viojsOua+dZ2PYKJ1CLZxn/evNVfoZG9TCudePelNWUAvnT1q4td+eemrCVqF2S/n0UM3FK6J1nunTjKL+ohbOm17217GhtyetTuzhKpx7Dpu5ZRLYVlD11oLi1HWHamqv/qJXcOqbfUc8eVtgs0YyL2c2EiABMxCgBzJDL2vaxmNlF99ZWjhxYUHpqdpbOzaf+EL4tJfuDOsaqKkRrIwESMAIBOiBjNBLBrHxytW6hZ8ffWnW7k35FVC4PfdIp4/f7v9gXw/f+hik0TSTBEjAcwL0QJ6z45WWBL7YVvbCeztXbjiBk4//ouPS8RFDB3YgIhIgARJwQoAeiMPDWwL5JdWIbpC8uqSi+nL/sNaIbvDmMz3atrYf283byng9CZCAHxGgGtt+Z+pH3KlnNXb52ctQWiO0KCB2aNMESmuEFlXv7jBKp1CNrd4YcFSyfsYG1dju9b5ONHmSGVRjG0WN/a+sY4+NyRVK67QvjtbVWQ8lz2S13oQE9Xn0SWE81dhUY+vtuapbe9RdhSsuLh72vykhIcE938jceiXwza7y4dN3pX15DE7ngT5t0sZF/P7X3Ro21Ku5tIsESECvBNT1QGh1UFDQ8vqUkpKiVwi0Sy4B7F46bsH305cVnayoxe6l2MN09NBuXdo1lXs985EACZCABQHVPRBp+weBs+ev/P2T0lFz9+YVnm0T2HjU06FzR/WJDG/jH61jK0iABHxCQHUPVFVVJdbhkpOTfdJCVuoNgYCAgMzMzA17a6G0/s+WHysObdnwwaAlEyJi7u/kTbG8lgRIgARAQF0PFBYWJpbgkPLy8nJycgjdKARqf7q2ee+Zl8YueCImZsGyLHzsULd/T/rYjIyMZk1uMkoraCcJkICeCWinxsYcKDQ0NDY21hbHkfoknQ8JCbGLDLpkaC61+cpJn/m3GacqrxYcv3zgxJWDJy4LCJj35KePfeZ3r/172Xyk6OhoSzj+TcPdW1fQGLmg/MNX2ltdqzgo0w5RzzpFs+cG1djudZBmKr34+PiioiKX1VGNrb0a+/KVa1v2n5m94sAL7+UJdbX4h9+ZLv/6eNHxmpEjR2JUTZ482bb7FJdcU41tCdkPaOhEIu9zM1w++syZQd1VuPT0dEmNHRcXh0U599wjc6tJ4Pjp2k83n5rwccET47b+ZdGBL3acOVVxKbhVk8eiOox/rufaaffNHnF3/K+6Fu3ZBB0j3M/UqVPxTkhNi1g2CZCAuQio64Gw5ia9B7K7/mYu2Dpo7fXrDXYcrJqXfhjxQ/8wc1fqusPbD1Thx6S9urdERAPI21ZNjnrr2bCH+rdv2fzGTgpwOTExMVh8S0pKwhsgHNMJ6aAbaQIJ+AkBdT2Qn0AyfjN+OHMpY8uPkxcfiH93//h/FGDjOOyh0KpFo4fvaf92fNjqpHv/9kYfeCD8xMeqrXA5cDzi3c+QIUOEEzI+D7aABEhAFwTogXTRDSoZsbu4+h+fHXl1dj601HM/Kd2yv/Ly1bqetwQOe6Qr4od+MvW+cb/r+Whkh6CWjR0ZUFdXB8cjfYtjnFHJWhZLAiRgNgLaaeFkks3Ozo6IiJCZWb1s+gl06G5k0opzV/JLavBvd+l5SKgFomY339Q/NLBfj5b4166VQ3/jiKdxaagxQlzSYGRSNbA7L9Nlp2hjEsygFs4t1Hr0QFZ6X6k9NTU1LVtaLxOJbxX/CrI9RyNJ8bqcFCjfjH2HzuUVViFgQdHx8xKx20NaIGxBZHgQNk3wBpR8MywHn+KgjGLGY3/KzXp/gNV9aFoadp9HJqTh1nPZPJm5Cmfgvq6qufJV3mlEaXv6L9vqldMn4H6aNA64945WiJqzZHzER2P6/fcT3SX3Y+Cm0nQSIAF/JEAPZLxeRXjQpVnHxy0s+a+k7bNWFCNS9bkLV7t1bD70gZD3/rvXZ9N/+ednuyNqTue2DBhqvM6lxSRgKgL0QMbo7pqLVzfuLv/ryuK4KTsQHnTJ+mOFxy8GBDS8986gEU/etmjsPQvf7v967G1RdwRxlwRj9CitJAESUDsuHAl7TECEBD1WcXXFhhNjUvc/8LsPHr6nY9aO05XnLoe0a/rbAZ3HxXf/bPov3n2511ODQm7p0MzjinghCZAACfiKAOdAviLvrN4rV+vGz/gnQoK+9dfMRZ8f/earL/LXjX06IeWVmO4L/tT/n+Mi3hh6e1R4q8aN2H167D7aRAIkIJOAHrVwZlZjl1Vdzso7sz6v8uJP126EBF039pGhIzZ8mrp0+crfDvmNzE5VPJt+pK7uatMVR4ECXdKgGlsN7M7LdNkp2phENbbbnPUWDs+0kUn3H6qesaxQigr61rx9m/LLGRJU+zitokZvQoI+OiZHgxCuhYWFjm5ehouVGd1VcVBOOkVvT1qd2MNlHLd9tuIXbPm++u35+0d/uO/rneUo/JGI9nNG9p712t01J7YxJKjitFkgCZCAfgjQA/msL/CyB6GpX5q16/01RxE+p0XTm+Ie6rJ0QsTYYT3vuq0VQ4L6rGNYMQmQgFYE6IG0Im1Rz4+Vlz7+7Mgzk7cjNPWxstqu7W6GonrNlHtffqJ7p+Cff8TDkKA+6BhWSQIkoC0BeiBNeX9/+NzM5UXPv7tz1caTFy5dQ7SCSS+Ezx0ZDkW1lbCNIUE17RhWRgIk4AsC1MLZp664tAYve9bnndl3+OegbQ/2CRocGXxHtxZGUfgYQoSmzR3kcmxQC6dNR1jW4rJTtDGJWji3OetEESGZ4WdaOGyAvfbbk3+YuVOI3GLHf/ePjMM/nKmVqdWh3olaOEd3KMeGscaG3p60OrGHq3Bu+2yZF8h52SOzKGYjARIgAb8kQA+kfLfKf9mjfN0skQRIgASMQ4AeSMm+cvTLngf6tlOyGpZFAiRAAn5BgB5IgW50/sseBSpgESRAAiTgjwTogbzqVb7s8QofLyYBEjA3Aaqx7fe/S3HnwWMXED90094qcX3v2wIHR7a9/66fN8NWalC5NEOpipyXQzMs+bikQTW2NsPSrU7RxiSqsd3mrBNNnoHU2F9+dxxhQ6UQoggniqCiLsNZehYDkYpbYyluRS8zMqlKt4M34WLtPug8uys9M0NvT1qd2KP6KlxaWtqw+pScnOy2e9TTBXzZo6feoC0kQAL+QEBdD1RcXJyVlbW8PpWWlubk5BiRGV/2GLHXaDMJkID+CajrgXJzcyMjIwWFqKiokpISAxCp3x5b2Ilf9rz41oLObZu7DOOm/3bRQhIgARLQGwF1PRBaGxwcLNocFBRUWVmpt/bb2pORkYG41AtXfoU9e55L/Cjt/df6PTlT2rOHv+zRfw/SQhIgAaMQUFcLh5dAADF8+HD8n56ejoW4xMREWzRH6pM436hRo6tXr/oW36wlO75YPPb2X7546LvFz46YETfkvjbNr/vWJNZuIAKbi24a1POagQymqUoRCAwMlFZ9lCrTz8tRVRGxePHi2bNniypwjOSyOieRSV1eq2CG3//+9+j4yZMnK1imB0XphAbNsOw70iANR/eyTsaGB48aX12i7ipcjx498vLyhA/fsWMHPhrCn+M90JIlS+B+pk6dKr0TMoTlNJIESIAEDERAXQ80cOBAzEmFGhtKBHzUPxqxPfZ7772XlJQk3gnRCem/12ghCZCAEQmo+x7IAyJ4IdS9e3cPLlTqkoCAADieu+66S5ghHBJ2LFWqfLfK8TkNYS3NsOw10iANR3exTsaGWw8Z32bWnQfyLQ7WTgIkQAIkoBkBdVfhNGsGKyIBEiABEjAcAXogw3UZDSYBEiABPyFAD+QnHclmkAAJkIDhCNADGa7LaDAJkAAJ+AkBeiA/6Ug2gwRIgAQMR8D3WjhE7kH8bIDDL4ekmD0JCQlVVTc2f4uLi4uNjdUAq60Z0hnUjtjeGtggVYHm4zglJQX/I6B4amoqDhBYT5zRLFmagaBKq1atQtWhoaHTpk3TzAZUZGmGqNf2jAb2WFU6adIkRJlCvY899piIO6VNstspqHrKlClhYWEa2CA1HHWNGDECP/JDCHz8fFtUrdmdYmuGT+4UWzMEB3FeMxoa9LtKVfh+DiT6CQnREzCURefh56vipDbuB5VamWG5rwRcowhwp03Csx5PeamuFStW4D4HCpz0oRnoHdEjCC8LC7VBgVqsaNg9o4ExVmZgsyv8QSCAaOl+rMzA3wRwPLABXhA/YtOAg6hCDEgk8RtzBBDBX4rCDC23AbMyY/369cIqREPW8k6xMgNA4AsxPDTrDkNX5HsPJP6gFr4Hf8ThAM84Le9q0X9WZlj9OanleMKMEL+BFVaJHZXEfX7vvfeKP7q1SZZmSHxwYOkdNbDEygzUaHtGezPgj+3G2FXbEqu2Ww5LKQi92jZYlY8bFsNS/KU4YMAALYeolSXS1FzjIWoLHH81+mR4aNz1ilTnew8kNlHFLB5/SqBJZWVlWH8TgXyQhGfSIFmZgRrxZ52wAfe2ZlMx/AmJPyQt2ys9WTp27KjZ9ha2Zkgm4eHbq1cvDXoEVdia4cQw9UyyqlSMSWmIarbvom3b4+PjcePAEo3/aMOysGi+YC45QvzdJhbPtUlWZkiVahyC0soMPEmwhKMNAT+oxfceCNMdMXdGR4qbGX/CiDNari3YmoG/5mAJbMAfnto4QjQfN7Bm3s7R8HVihngIavO+wdYMn/CxW6m0BIc/U7D4o8GDwK4Z2PIRlsAG/FmgmSPEVEPcnlid1nLNzXbGY9cMOADctpqFoLSigQcF/J/2SzgajECVqvC9B5Iahkcb7ijLv/QRS1vLP6mEJcIMccNjeGEw4Q7HSrdKHWBZLOqF2xMzQjERxLfSvAezQ21WWuyaAUssd3vyCQ1HhqlqjG2lln/pYzqozcTU1gzxsIM4BX+yYP0AKz+qcrAtHMvC4vaUblKYpOV6tTBJMgPHTjYhUxuOMKOgoEBawkGNWq7iqN1Atcr31bYQot7NmzdLmwbhLlq3bh1OYm2hqKgIB9hbSM6WQt43wdYMWAJ7pJ2NpF2OvK9LTglovlQ7aMA8LWlIFlqagY6YOHGiHOMVz2Nphijc9ozildoWaFkpekd0iuUOWBrYYNl2GICxISrFcNW+d6TbU7pztadheV9Y3rPa9IVlLbYPK6l3tDfGQDX6Xo0tCa8lVatPhL+2ZljqLDHfV+tPAHvl4m/JOXPmCO21T2gIoyQzLOW2OK+xINuShpVhvuoUnwh/bduORTBp/y3N1NjS6x9pGPiEhq0Z0hmA0uynC7ZmSGMSX2n83NDydlCqLt97IKVawnJIgARIgASMRUBH74GMBY7WkgAJkAAJeEmAHshLgLycBEiABEjAQwL0QB6C42UkQAIkQAJeEqAH8hIgLycBEiABEvCQAD2Qh+B4GQmQAAmQgJcE6IG8BMjLSYAESIAEPCRAD+QhOF5GAiRAAiTgJQF6IC8B8nISIAESIAEPCdADeQiOl5EACZAACXhJgB7IS4C8nARIgARIwEMC9EAeguNlJEACJEACXhKgB/ISIC83BgEEeJWzmQ3C0YqNdhCp1uWmUChQyw3LjQGaVpKAOwTogdyhxbz6JgD/ITYxkpngY+BppMyWe6LLKQGbqWP3Qjk5mYcESMAuAXogDgz/ISB2FPS4PdgFDjsOyL9c7BWr2eak8g1jThIwCgF6IKP0lOnsxGxGWjfDTEVa75J2ZMG3OEaSsknLYvAK4iuRJCeBcvBRzHvEpkdiR0tRAjaoxba8VqDxrZhXwQDLMsUaHTzWmTNnTNc3bDAJKESAHkghkCxGaQIDBgyASxCuAtuTi2P4EjFNgVfASewAJjYBs3ofgy2rsXEnvsK2h0gDBw5EHmzmNnr0aJzEhciPGQx2dcNWZjiTmJgoPBA2ibdsB3wV9mgX86pVq1YhPzJHRkbipJgASYYp3XqWRwKmIEAPZIpuNmIjpTWugoICPPQxWUErsFCGY+Et8A5GTErgWsS3tqmyslI6iQtFmfBhjvJbloAZErxXbGysVbFyrjUicNpMAtoToAfSnjlrlEsgKioKLgfOplevXpisYAK0Y8cOHIvrMRERcyAkq9c/8DGpqalwTrjW4zdDKB/zHslWlAmfJNYAbd2S3CYxHwmQgAUBeiAOB/0SwFsZuBDMOTB3gQPYvn07Vr2keQymPo5Mx1fCM6WkpDhvnuWEBk6urKxMyg9XByckvTTCdEqUCb2DlAcnYZJ+CdIyEtA3AXogffePua3D+xs84uEYgAH+AH5F0qqJmY2t1kAAQzbpK0i0HVEUjk1SIuAYUy7LzJjr4CRKEG5PKlPSPtgVL5i709h6EnCHwHUmEvAvAps3b4YMQWpTfHx8UVGRnCbiwokTJ9rNuW7dOukrlIYykQ0HlhXJqYJ5SIAELAk0xAd3HBbzkoABCGDWIrRzSFATyH8VhAsHDx4stHNWCctx0pIdVucwPcJMCDMkvhMywICgiXolQA+k156hXSRAAiTg7wT4Hsjfe5jtIwESIAG9EqAH0mvP0C4SIAES8HcC9ED+3sNsHwmQAAnolQA9kF57hnaRAAmQgL8T+B8H1zoICs5eLAAAAABJRU5ErkJggg==)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOwAAAABCAMAAAGd0ILsAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAGUExURURyxERyxL0AA4oAAAABdFJOU78bOHZ7AAAACXBIWXMAAA7DAAAOwwHHb6hkAAAAF0lEQVQYV2NgYMQHKJHFDyjRSzZgZAAAbg0A66YbNpIAAAAASUVORK5CYII=)
Observe, from the graph the vertical line parallel to y-axis touches y-axis at 46.5 (approx.).
Hence, median is 46.5.
Finding median by formula:
![](data:image/png;base64,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)
For median:
We have, total frequency, N = 35
N/2 = 35/2 = 17.5
Observe, cf = 28 is just greater than 17.5.
Thus, median class = 46-48
Median is given by
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAMwAAABGCAMAAAC314t+AAAAAXNSR0IArs4c6QAAAKJQTFRFAAAAAAAAAAA6AABmADpmADqQAGZmAGa2OgAAOgA6OgBmOjoAOjpmOmY6Oma2OpDbZgAAZgA6ZjoAZjo6ZjpmZmY6ZmaQZpC2ZpDbZra2ZrbbZrb/kDoAkDo6kGYAkGY6kLbbkNu2kNvbkNv/tmYAtmY6tmZmttv/tv//25A625Bm27Zm27aQ29uQ29u22/+22////7Zm/9uQ/9u2//+2///bNSyZSwAAAAF0Uk5TAEDm2GYAAAAJcEhZcwAADsQAAA7EAZUrDhsAAAAZdEVYdFNvZnR3YXJlAE1pY3Jvc29mdCBPZmZpY2V/7TVxAAADwUlEQVRoQ+2be3fSMBTAk8Kk6uQ18TFQ59rpOtHRQr7/V/Pe3CQUSkuCHJbW5I/RntPH/eW+b88YCyvsQHkHNmMeJYyJBefzFu8MYHDee4SfAVBsxlYsGdzjI/VmfLVCiskMpRMLKxi4IfMa5n4BVF2BSXI+6g4MS6OkM5phRTzoDgw49W1HAoBMM/1pN6IZwLDcPnt4HZopW6YW2UN84xD3PIbBOgBpiviomYnFgGVewzjUY4rXY804wORkiS2HKaacR/M8phqz3TBFfMvWECY6oZlUVtcYvn03M+xP9JIip+YUmzbZ6YzIsfyHOR4AAszxPTrvFarTZGIJwapPJnVoYa5sjZmlHINV77GWBkpqJn4krfCZFDe+MXk8xbx/h7WoDGf+5xkVqWwM2X+YtMHM9gi9h7GomQ2S7zBiofLiRczMoRG0kUdldlWmQNOsgq/VvbWayeSgVz1bd64wAq1slHRQBy+FR+L4uElInWegghmsrDDoonozyw0M1ECc5qXjKgs1gm4w8KA9lt1xkoHJ8LW5taHZwUxmkix/Na0+2MVD9S5XrOcwTPEaxzPpCTCb95Rp1+q3rJnJd6xPxeIzlanQEkWf1AF/B5ohxxG/3nI+pHkKZDM4qluWMKpMPgEGBlRIsxkrIfLo/kG5yGaSYLTPr54lDLZESzQuPBBfkQPVAxKuBIxT8ew6aUzHljAO7rLvMwJH7ltrzvn1T5INvi3ABHvO0hHV3NgSSXFkbyTdxdiaPFB/1I5W2hDUsZ3PONKUfQZo/kxN+ChFKYCB1xdv4PMPCGiI6GArvjQ8A2OajQMS7cBUYSkAlJszi+P9aAYhUwd42HEyGCzgAIZlvdmIOOR3LfqytQsjljcwWdCasYZB2Jpo9g+awfhfC1PEAFfSjHSvHRj0mUOaqTUz8cW0KueHkWZmaPY0A/lLiW9shA6Mz2xvkPo8rhlUuFpnh9EBAMwVVxlGfyIlAXNsiZ4gNmfRHVvf6AqgiEdsPTMpFE/rFoWZbFsPnxtGsuCGlltRue166CsPUEJIItFHuFg88Gj4O+bzQvoKRPLh81id6WsP8WA5Q253gmZoRn5wbaPZ+gOppKBfyHxRQkJefG1rs+qr1Yz8CMzFRa5/YRNMU/Xkez9TIW4qadsGo2fk3TCzLmmmsXNqm5kFmBcN1E2hOfjMS6rmf9GMnpF3I880WUzrQnOA8TUABM0EzZxpB5ryTDCzM23ySY8JmoFtC0nzJNtxuCmYWTAzB3M59VL1z0But/v6z0BuFE5X/wWa8o4/jsY03AAAAABJRU5ErkJggg==)
Where,
L = Lower class limit of median class = 46
N/2 = 17.5
cf = cumulative frequency of the class preceding median class = 14
f = frequency of the median class = 14
h = class interval of the median class = 2
Substituting these values in the formula of median, we get
![](data:image/png;base64,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)
⇒ ![](data:image/png;base64,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)
⇒ Median = 46 + 0.5
⇒ Median = 46.5
Thus, median is 46.5.
Hence, verified.
Question 3.the following table gives production yield per hectare of wheat of 100 farms of a village.
![](data:image/png;base64,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)
Change the distribution to a more than type distribution and draw its ogive.
Answer:Let’s make more than type cumulative frequency table:
![](data:image/png;base64,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)
Plot points (50,100), (55,98), (60, 90), (65, 78), (70, 54) and (75,16) on a graph.
![](data:image/png;base64,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)
The following distribution gives the daily income of 50 workers of a factory.
Convert the distribution above to a less than type cumulative frequency distribution, and draw its ogive.
Answer:
Let’s make less than type cumulative frequency table:
Plot points (300,12), (350,26), (400, 34), (450, 40) and (500,50) on a graph.
Question 2.
During the medical check-up of 35 students of a class, their weights were recorded as follows :
Draw a less than type ogive for the given data. Hence obtain the median weight from the graph and verify the result by using the formula.
Answer:
Using points (38,0), (40,3), (42,5), (44,9), (46,14), (48,28), (50, 32) and (52,35), plot a graph.
To find median graphically,
We have total frequency, N = 35
⇒ N/2 = 35/2 = 17.5
Plot 17.5 on the y-axis and draw a horizontal line intersecting the ogive parallel to x-axis.
Observe, from the graph the vertical line parallel to y-axis touches y-axis at 46.5 (approx.).
Hence, median is 46.5.
Finding median by formula:
For median:
We have, total frequency, N = 35
N/2 = 35/2 = 17.5
Observe, cf = 28 is just greater than 17.5.
Thus, median class = 46-48
Median is given by
Where,
L = Lower class limit of median class = 46
N/2 = 17.5
cf = cumulative frequency of the class preceding median class = 14
f = frequency of the median class = 14
h = class interval of the median class = 2
Substituting these values in the formula of median, we get
⇒
⇒ Median = 46 + 0.5
⇒ Median = 46.5
Thus, median is 46.5.
Hence, verified.
Question 3.
the following table gives production yield per hectare of wheat of 100 farms of a village.
Change the distribution to a more than type distribution and draw its ogive.
Answer:
Let’s make more than type cumulative frequency table:
Plot points (50,100), (55,98), (60, 90), (65, 78), (70, 54) and (75,16) on a graph.