Question

The following table shows the profit made by a group of shops in a mall. The median of the data 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

Firstly, the cumulative frequency (CF) table is drawn.

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

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

C.F nearest to 50 and greater than 50 is 57.

$\therefore Median=l+\left(\frac{\frac{n}{2}-cf}{f}\right)\times h$
Where $l$ is lower class limit of median class.
$n$ is total number of observations.
$cf$ is the cumulative frequency of the class preceding the median class.
$f$ is the frequency of the median class and h is the class size.
$Median=20+\left(\frac{50-30}{27}\right)\times 10$

Median = 27.4