Question

Find the median for the distribution given below.

$$\begin{array}{cccccc}\text{Wages}& 200-300& 300-400& 400-500& 500-600& 600-700\\ \text{Number of labourers}& 3& 5& 20& 10& 6\end{array}$$

• A. 470

Answer 1

The correct option is A 470

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

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.

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

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 distribution,

$l$ = 400

$n$ = 44

$cf$ = 8

$f$ = 20

$h$ = 100

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

$=400+\frac{(22–8)}{20}\times 100$

$=400+70$

$=470$

$\therefore$ The median is 470.