Question

Find the inter quartile range for the following Data

$\begin{array}{ccc}\text{Class}& \text{Frequency}& \text{Cumulative Frequency}\\ 10-20& 4& 4\\ 20-30& 3& 7\\ 30-40& 2& 9\\ 40-50& 1& 10\\ 50-60& 5& 15\end{array}$

• A. 20
• B. 54
• C. 34
• D. 50

Answer 1

The correct option is C

34

$\begin{array}{ccc}\text{Class}& \text{Frequency}& \text{Cumulative Frequency}\\ 10-20& 4& 4\\ 20-30& 3& 7\\ 30-40& 2& 9\\ 40-50& 1& 10\\ 50-60& 5& 15\end{array}$

Here N =15
$\frac{N+1}{n}=\frac{16}{4}=4$ which lies in 10-20
Upper quartile =$\frac{3}{4}(N+1)=\frac{3}{4}\times (15+1)=12$
$Q_1=4^{th}$ term =20
$Q_3={12}^{th}$ term =54
Inter Quartile range =$Q_3-Q_1=54-20=34$