Question

Find the median for the distribution given below.

$$\begin{array}{cccccc}Class& 200-300& 300-400& 400-500& 500-600& 600-700\\ Numberofstudents& 3& 5& 20& 10& 6\end{array}$$

• A. 300
• B. 420
• C. 400
• D. 470

Answer 1

The correct option is D

470

First a less than frequency distribution is drawn as shown below.

$$\begin{array}{ccc}Wages& Frequency& Cumulativefrequency\\ 200-300& 3& 3\\ 300-400& 5& 8\\ 400-500& 20& 28\\ 500-600& 10& 38\\ 600-700& 6& 44\end{array}$$

In the above distribution the total number of observations (labourers) is 44. Hence n = 44.

$\frac{n}{2}$ = 22.

The cumulative frequency that is greater than 22 but closest to 22 is 28. The class corresponding to this frequency is 400-500. This is the median class.

Median = l + $\frac{(\frac{n}{2}-cf)}{f}$$\times$ h,

where

l = lower limit of median class,

n = number of observations,

cf = cumulative frequency of class preceding the median class.

f= frequency of median class.

h = class size (assuming class size to be equal).

For the given class,

l = 400

n = 44

cf = 8

f = 20

h = 100

Median = 400 + $\frac{(\frac{44}{2}-8)}{20}$ $\times$ 100

= 400 + $\frac{(22–8)}{20}\times$ 100

= 400 + 70

= 470

$\therefore$ The median is 470.