Question

Find the quartile deviation of the following cumulative frequency distribution:

$\begin{array}{ccc}x& frequency& Cumulativefrequency\\ 22& 1& 1\\ 34& 2& 3\\ 39& 2& 5\\ 45& 8& 13\\ 54& 8& 21\\ 56& 9& 30\\ 68& 4& 34\\ 78& 4& 38\\ 84& 2& 40\end{array}$

• A. 10
• B. 11.5
• C. 20
• D. 23

Answer 1

The correct option is A 10

$Q_1=sizeof\left(\frac{N+1}{4}\right)thobservation=sizeof{10.25}^{th}observation=45$

$Q_3=sizeof3\left(\frac{N+1}{4}\right)thobservation=sizeof{30.75}^{th}observation$

Here, size of 30th observation is 56 and the size of 31st observation is 68.

$sizeof{30.75}^{th}observation=56+0.75\times (68-56)=56+9=65$


$Quartiledeviation=\frac{Q_3-Q_1}{2}=\frac{65-45}{2}=10$