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. 30.7
• B. 24.8
• C. 31.2
• D. 27.5

Answer 1

The correct option is D

27.5

Cumulative frequencies are given by :

$\begin{array}{ccc}\text{C.I}& \text{Frequency}& \text{CF}\\ 0-10& 12& 12\\ 10-20& 18& 30\\ 20-30& 27& 57\\ 30-40& 20& 77\\ 40-50& 17& 94\\ 50-60& 6& 100\\ & \text{Total}& 100\end{array}$

$\frac{n}{2}=\frac{100}{2}=50$

n = 100

The median for grouped data is formed by $\frac{n}{2}$ = ${50}^{th}$ Observation.

Let's draw an ogive and plot the points on it.

The median of the given Data is - 27.5 as seen from the Graph