Question

The distribution below gives the weight of 30 students in a class. Find the median weight of students:
Weight (in kg): 40-45 45-50 50-55 55-60 60-65 65-70 70-75
No. of students: 2 3 8 6 6 3 2

Answer 1

We may find cumulative frequency with their respective class intervals as below

Weight (in kg)	Number of students $f_i$	Cumulative frequency (cf or F)
40 – 45	2	2
45 – 50	3	5
50 – 55	8	13
55 – 60	6	19
60 – 65	6	25
65 – 70	3	28
70 – 75	2	30

Cumulative frequency just greater than $\frac{N}{2}$ (i.e.

$\frac{30}{2}=15$) 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 or F) = 13

Class size (h) = 5

$Median=L+\frac{\frac{N}{2}-F}{f}\times h$

$=55+\frac{15-13}{6}\times 5$

$=55+\frac{10}{6}=56.666$

So, median weight is 56.67 kg