Question

Find the median of the given data:

$\begin{array}{cccccc}\text{Wages in (Rs.)}& 200-300& 300-400& 400-500& 500-600& 600-700\\ \text{No. of Labourers}& 3& 5& 20& 10& 6\end{array}$

• A. 300
• B. 420
• C. 400
• D. 470

Answer 1

The correct option is D 470

Less than frequency distribution for the data is :
$\begin{array}{cc}\text{Wages less than (Rs.)}& \text{Number of Labourers}\\ 300& 3\\ 400& 8\\ 500& 28\\ 600& 38\\ 700& 44\end{array}$

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

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

$Median=400+\left[\frac{22-8}{20}\right]\times 100$
$=400+(22–8)\times 5$
= 400 + 70
= 470
The median is 470.