Question

Find the median of the following data.

$$\begin{array}{cccccc}Classinterval& 0-10& 10-20& 20-30& 30-40& 40-50\\ Frequency& 10& 9& 8& 17& 6\end{array}$$

• A. 20
• B. 50
• C. 54
• D. 27.5

Answer 1

The correct option is D 27.5

$$\begin{array}{cccccc}Classinterval& 0-10& 10-20& 20-30& 30-40& 40-50\\ Frequency& 10& 9& 8& 17& 6\\ Cumulativefrequency& 10& 19& 27& 44& 50\end{array}$$

In the above distribution the total number of observations is 50.
$\therefore N=50⟹\frac{N}{2}=25$.
The cumulative frequency that is greater than 25 but closest to 25 is 27. The class corresponding to this frequency is 20-30. This is the median class.

$\text{Median}=\text{LRL}+\left(\frac{\frac{N}{2}-f_c}{f_m}\right)\times i$,
where LRL stands for the lower real limit, $f_m$=frequency of median class, $f_c$=cumulative frequency above the median class and $i$=size of the class interval
$⟹Median=20+\frac{25-19}{8}\times 10=27.5$