Question

Find the median of the given data:

$\begin{array}{cccccc}Wages(inRs.)& 200-300& 300-400& 400-500& 500-600& 600-700\\ No.ofLabourers& 3& 5& 20& 10& 6\end{array}$

• A. 300
• B. 420
• C. 400
• D. 470

Answer 1

The correct option is D 470

Less than frequency distribution for the data is :
$\begin{array}{cc}WageslessthanRs.& NumberofLabourers\\ 300& 3\\ 400& 8\\ 500& 28\\ 600& 38\\ 700& 44\end{array}$

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

In the above distribution the total number of observations (labourers) is 44.
$\therefore N=44⟹\frac{N}{2}=22$.
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.
$\text{Median}=\text{LRL}+\left(\frac{\frac{N}{2}-f_c}{f_m}\right)\times i$,
where LRL stands for the lower real limit, $f_m$=frequency of median class, $f_c$=cumulative frequency above the median class and $i$=size of the class interval
For the given class,
LRL = 400, $N=44$, $f_c=8$, $f_m=20$ and $i=100$
$⟹Median=400+\left[\frac{22-8}{20}\right]\times 100$
$=400+(22–8)\times 5=400+70=470$
Therefore, the median is 470.