Question

Medical check-up was carried out for 35 students of a class and their weights were recorded as follows:

Weight (in kg):	38-40	40-42	42-44	44-46	46-48	48-50	50-52
Number of students:	3	2	4	5	14	4	3

Find the difference between the mean weight and the median weight.

Answer 1

Using the class marks 39, 41, 43, 45, 47, 49 and 51:

\[\sum f_i x_i=1603,\qquad N=35\] 

\[\text{Mean weight}=\frac{1603}{35}=45.8\text{ kg}\] 

The cumulative frequency first exceeding `N/2 = 17.5` is 28, so the median class is 46–48. 

Here l = 46, h = 2, f = 14 and F = 14.

\[\text{Median weight}=46+\frac{17.5-14}{14}\times 2=46.5\text{ kg}\] 

\[\text{Difference}=|46.5-45.8|=0.7\text{ kg}\]