Question

The below table shows that profit made by a group of shops in mall. Then the median is

$\begin{array}{ccccccc}\text{Profit per shop less than}\left(\%\right)& 10& 20& 30& 40& 50& 60\\ \text{No. of shops}& 12& 30& 57& 77& 94& 100\end{array}$

• A. 27.4
• B. 31.2
• C. 26.8
• D. 23.7

Answer 1

The correct option is A

27.4

Cumulative frequencies are given by

$\begin{array}{ccc}\text{C.I}& \text{CF}& \text{Frequency}\\ 0-10& 12& 12\\ 10-20& 30& 18\\ 20-30& 57& 27\\ 30-40& 77& 20\\ 40-50& 94& 17\\ 50-60& 100& 6\\ & Total& 100\end{array}$ $\frac{n}{2}=\frac{100}{2}=50$ CF nearest to 50 and greater than 50 is 57 $\therefore \text{Median}=l+\left(\frac{\frac{n}{2}-cf}{f}\right)\times h\text{Median}=20+\left(\frac{50-30}{27}\right)\times 10$ Median = 27.4