Question

Find the quartile deviation 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. 62.5
• B. 67.5
• C. 75
• D. 100

Answer 1

The correct option is B 67.5

The cumulative frequency distribution for the data is :

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

In the above distribution the total number of observations (labourers) is 44. Hence N = 44.
$\frac{N}{4}=11\&\frac{3N}{4}=33$

Class corrsponding to the first quartile is 400 - 500
$Q_1=L+\frac{\frac{N}{4}-cf}{f}\times h=400+\frac{11-8}{20}\times 100=415$

Class corrsponding to the third quartile is 500 - 600

$Q_3=L+\frac{\frac{3N}{4}-cf}{f}\times h=500+\frac{33-28}{10}\times 100=550$

$Quartiledeviation=\frac{Q_3-Q_1}{2}=\frac{550-415}{2}=67.5$