Question

Find the inter quartile range, quartile deviation and coefficient of quartile deviation from the following data:

$\begin{array}{cccccccc}\text{Marks}& 28& 18& 20& 24& 27& 30& 15\end{array}$

Answer 1

First arrange the data in ascending order:

$\begin{array}{cc}\text{S.No}& \text{Marks}\\ 1& 15\\ 2& 18\\ 3& 20\\ 4& 24\\ 5& 27\\ 6& 28\\ 7& 30\\ \text{N=}7& \end{array}$

$Q_1=$ Size of $\left(\frac{N+1}{4}\right)th$ item = Size of $\left(\frac{7+1}{4}\right)th$ item

= Size of 2nd item = 18 marks

$Q_3=$ Size of $3\left(\frac{N+1}{4}\right)th$ item = Size of $3\left(\frac{7+1}{4}\right)th$ item.

= Size of 6th item = 28 marks.

Inter Quartile Range $=Q_3-Q_1=28-18=10$

Quartile Deviation $=\frac{Q_3-Q_1}{2}=\frac{28-18}{2}=5$

Coefficient of Quartile Deviation $=\frac{Q_3-Q_1}{Q_3+Q_1}=\frac{28-18}{28+18}=\frac{10}{46}=0.217$