Question

The first and the third quartiles of the data given below :

Marks	No. of Students
0-10	4
10-20	8
20-30	11
30-40	15
40-50	12
50-60	6
60-70	3

are respectively

• A. 21.5, 43.8
• B. 26.26, 49.69
• C. 22.5, 45.2
• D. 23, 45

Answer 1

Answer: (C)

Here, we construct the cumulative frequency table

Class	Frequency	Cumulative frequency
0-10	4	4
10-20	8	12
20-30	11	12
30-40	15	38
40-50	12	50
5-60	6	56
6-70	3	59

For $Q_1$. Here $n=59 \Rightarrow \frac{n}{4}=\frac{59}{4}=14.75$
$\therefore $ Class of first quartile is $20 - 30$
$\Rightarrow Q_{1}=20+\frac{14.75-12}{11}\times10=20+\frac{27.5}{11}=22.5$
For $Q_{3}$. Here $\frac{3n}{4}=\frac{3\times59}{4}=44.25$
$\therefore $ Class of third quartile is $40-50$
$\Rightarrow Q_{3}=40+\frac{44.25-38}{12}\times 10=40+\frac{62.5}{12}=45.2$