### Marks 10 20 30 40 50 No. of Students 4 7 13 8 6 1) Write the formula of Q1 and Q3. 2) Find out the median of the above data? 3) Find out the cumulative frequency of the last value in the above data. 4) Find out the value of 'n' in the above data - Economics

#### QUESTION

Answer the following questions on the basis of the given data :

 Marks 10 20 30 40 50 No. of Students 4 7 13 8 6

1) Write the formula of Q1 and Q3.

2) Find out the median of the above data?

3) Find out the cumulative frequency of the last value in the above data.

4) Find out the value of 'n' in the above data

Sum

#### SOLUTION

 Marks No. of Students cf 10 4 4 20 7 11 30 13 24 40 8 32 50 6 38 N = 38

1. Formula of Q1

Q= Size of 1${\left(\frac{n+1}{4}\right)}^{\text{th observation}}$

Formula of Q3

Q= Size of 3${\left(\frac{n+1}{4}\right)}^{\text{th observation}}$

2. Median = Q2

Median = Q2 = Size of 2${\left(\frac{n+1}{4}\right)}^{\text{th observation}}$

= Size of 2${\left(\frac{38+1}{4}\right)}^{\text{th observation}}$

= Size of 2${\left(\frac{40}{4}\right)}^{\text{th observation}}$

= Size of 2 (9.75)th observation

= Size of 19.5th observation

= Size of 19.5th observation lies in cf 24

Hence, quartile value = 30 marks.

3. The cumulative frequency of the last value in the above data is 38.

4. The value of 'n' in the above data is 38.