OMTEX CLASSES: MERITS AND DEMERITS OF MEAN, MEDIAN AND MODE

Arithmetic Mean

The arithmetic mean (or simply "mean") of a sample is the sum of the sampled values divided by the number of items in the sample.

Merits of Arithmetic Mean

Arithmetic mean is rigidly defined by an algebraic formula.
It is easy to calculate and simple to understand.
It is based on all observations and can be regarded as representative of the given data.
It is capable of being treated mathematically and hence it is widely used in statistical analysis.
Arithmetic mean can be computed even if the detailed distribution is not known but some of the observations and the number of observations are known.
It is least affected by the fluctuation of sampling.

Demerits of Arithmetic Mean

It can neither be determined by inspection nor by graphical location.
Arithmetic mean cannot be computed for qualitative data like data on intelligence, honesty, and smoking habits, etc.
It is too much affected by extreme observations and hence it does not adequately represent data consisting of some extreme points.
Arithmetic mean cannot be computed when class intervals have open ends.

Median

The median is that value of the series which divides the group into two equal parts, one part comprising all values greater than the median value and the other part comprising all the values smaller than the median value.

Merits of Median

Simplicity: It is a very simple measure of the central tendency of the series. In the case of simple statistical series, just a glance at the data is enough to locate the median value.
Free from the effect of extreme values: Unlike arithmetic mean, median value is not destroyed by the extreme values of the series.
Certainty: Certainty is another merit of the median. Median values are always a certain specific value in the series.
Real value: The median value is a real value and is a better representative value of the series compared to the arithmetic mean (average), the value of which may not exist in the series at all.
Graphic presentation: Besides algebraic approach, the median value can be estimated through graphic presentation of data as well.
Possible even when data is incomplete: Median can be estimated even in the case of certain incomplete series. It is enough if one knows the number of items and the middle item of the series.

Demerits of Median

Following are the various demerits of median:

Lack of representative character: Median fails to be a representative measure in case of such series where the different values are wide apart from each other. Also, median is of limited representative character as it is not based on all the items in the series.
Unrealistic: When the median is located somewhere between the two middle values, it remains only an approximate measure, not a precise value.
Lack of algebraic treatment: Arithmetic mean is capable of further algebraic treatment, but median is not. For example, multiplying the median with the number of items in the series will not give us the sum total of the values of the series.

However, median is quite a simple method for finding an average of a series. It is quite a commonly used measure in the case of such series which are related to qualitative observations such as the health of the student.

Mode

The value of the variable which occurs most frequently in a distribution is called the mode.

Merits of Mode

Following are the various merits of mode:

Simple and popular: Mode is a very simple measure of central tendency. Sometimes, just looking at the series is enough to locate the modal value. Because of its simplicity, it is a very popular measure of the central tendency.
Less effect of marginal values: Compared to the mean, mode is less affected by marginal values in the series. Mode is determined only by the value with the highest frequency.
Graphic presentation: Mode can be located graphically, with the help of a histogram.
Best representative: Mode is that value which occurs most frequently in the series. Accordingly, mode is the best representative value of the series.
No need of knowing all the items or frequencies: The calculation of mode does not require knowledge of all the items and frequencies of a distribution. In simple series, it is enough if one knows the item with the highest frequency in the distribution.

Demerits of Mode

Following are the various demerits of mode:

Uncertain and vague: Mode is an uncertain and vague measure of the central tendency.
Not capable of algebraic treatment: Unlike mean, mode is not capable of further algebraic treatment.
Difficult: When the frequencies of all items are identical, it is difficult to identify the modal value.
Complex procedure of grouping: Calculation of mode involves cumbersome procedure of grouping the data. If the extent of grouping changes, there will be a change in the modal value.
Ignores extreme marginal frequencies: It ignores extreme marginal frequencies. To that extent, the modal value is not a representative value of all the items in a series. Besides, one can question the representative character of the modal value, as its calculation does not involve all items of the series.

Practice Problems: To Find Mean

Practice Problems: To Find Median

Practice Problems: To Find Mode

Relationship Between Mean, Median, and Mode

ALSO REFER THESE ECONOMICS QUESTIONS.

Difficult Words & Meanings:

Arithmetic Mean: The average of a set of numbers, found by summing all numbers and dividing by the count of numbers.
Median: The middle value in a dataset that has been arranged in order of size.
Mode: The value that appears most frequently in a dataset.
Sample: A small part or quantity intended to show what the whole is like; a selection from a larger population.
Values: The specific numbers or pieces of data in a set.
Observations: The individual data points or values collected during a study or survey.
Algebraic Formula: A mathematical rule or principle expressed in symbols or letters.
Qualitative Data: Information that describes characteristics or qualities and cannot be easily measured with numbers (e.g., color, opinions, gender).
Extreme Values/Observations: Data points that are significantly smaller or larger than other values in a dataset.
Class Intervals: The ranges into which data is divided for grouping (e.g., 10-20, 20-30).
Open Ends (Class Intervals): When the first class interval has no lower limit or the last class interval has no upper limit (e.g., "Under 10" or "50 and over").
Central Tendency: A statistical measure that identifies a single value as representative of an entire distribution (e.g., mean, median, mode).
Frequency: The number of times a particular value or event occurs in a dataset.
Distribution: The way in which data or values are spread or arranged.
Histogram: A graphical display of data using bars of different heights, where each bar groups numbers into ranges.
Marginal Values/Frequencies: Values or frequencies that are at the outer edges or extremes of a dataset.
Cumbersome: Complicated, slow, or difficult to do or use.
Fluctuation: An irregular variation or change in level, amount, or value.
Rigidly Defined: Clearly and precisely established, leaving no room for ambiguity.
Inspection (statistical): The process of carefully examining data to identify patterns or features without complex calculations.
Graphical Location: Determining a value by using a graph or chart.
Representative Character: The extent to which a single statistical measure (like mean or median) accurately reflects the entire dataset.
Approximate Measure: A value that is close to the actual value but not perfectly exact.
Vague (measure): Not clearly or precisely expressed; indefinite.
Identical (frequencies): Occurring when all values in a dataset have the same frequency (number of occurrences).