Question

From the following frequency distribution table, find:
(i) Lower quartile (ii) Upper quartile (iii) Inter-quartile range

Ci frequency
5-10 3
10-15 4
15-20 6
20-25 9
25-30 7
30-35 1

Answer 1

We write the variates in cumulative frequency table.

Variate

Frequency (f)

Cumulative frequency

15

4

4

18

6

10

20

8

18

22

9

27

25

7

34

27

8

42

30

6

48

(i) Here the number of observations, n=48 which is even.

So median=21(n/2thterm+((n/2)+1)thterm)

=21(48/2thterm+((48/2)+1)thterm)

=21(24thterm+(24+1)thterm)

=21(24thterm+25thterm)

=21(22+22) [Since all observations from 19th to 27th are 22]

=21×44

=22

Hence the median is 22.

(ii) Lower quartile, Q1=(n/4)thterm

=(48)/4

=12thterm

=2