Question

The distribution below gives the weights of 30 students of a class. Find the median weight of the students.

Weight (in kg)	40−45	45−50	50−55	55−60	60−65	65−70	70−75
Number of students	2	3	8	6	6	3	2

Answer 1

The cumulative frequencies with their respective class intervals are as follows

Weight (in kg)	Frequency (fi)	Cumulative frequency
40 − 45	2	2
45 − 50	3	2 + 3 = 5
50 − 55	8	5 + 8 = 13
55 − 60	6	13 + 6 = 19
60 − 65	6	19 + 6 = 25
65 − 70	3	25 + 3 = 28
70 − 75	2	28 + 2 = 30
Total (n)	30

Cumulative frequency just greater than `N/2 (i.e  30/2 = 15)` is 19, belonging to class interval 55 − 60.

Median class = 55 − 60

Lower limit (l) of median class = 55

Frequency (f) of median class = 6

Cumulative frequency (cf) of median class = 13

Class size (h) = 5

Median = `l + ((N/2 - cf)/f) xx h`

= `55 + ((15-13)/6) xx 5`

= `55 + 10/6`

= 55 + 1.66

= 56.67

Therefore, the weight is 56.67 kg.