Question

During a medical checkup, height of 35 students of a class were recorded as follows:

Height (in cm):	90-100	100-110	110-120	120-130	130-140	140-150
Number of Students:	3	2	4	5	14	7

Find the difference between the mean height and median height.

Answer 1

Using the class marks 95, 105, 115, 125, 135 and 145:

\[\sum f_i x_i=4485, \quad N=35\] 

\[\text{Mean height}=\frac{4485}{35}\approx 128.14\text{ cm}\] 

The cumulative frequency first exceeding `N/2 = 17.5` is 28, so the median class is 130–140. 

Here l = 130, h = 10, f = 14 and F = 14.

\[\text{Median height}=130+\frac{17.5-14}{14}\times 10=132.5\text{ cm}\] 

\[\text{Difference}=|132.5-128.14|\approx 4.36\text{ cm}\]