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. 27.59
• B. 34.2
• C. 24.8
• D. 31.7

Answer 1

The correct option is A

27.59

Cumulative frequencies are given by :

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

n = 100

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

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

It lies in the Class interval of 20-30.

If we take the step jump method , we get the two terms as :

$20+\frac{10}{27}\times 20$ and $20+\frac{10}{27}\times 21$

The median i.e. the 50th term is given by the average of these 2 observations.

Median = $\frac{(20+\frac{10}{27}\times 20)+(20+\frac{10}{27}\times 21)}{2}$

= $\frac{\left(\frac{(27\times 20)+200}{27}\right)+\left(\frac{(27\times 20)+210}{27}\right)}{2}$

= $\frac{740+750}{27\times 2}$

= $\frac{1490}{54}$

= 27.59

$\therefore$The median of the given Data is - 27.59