Question

Find the median of the following data.

$$\begin{array}{cccccc}Classinterval& 0-20& 20-40& 40-60& 60-80& 80-100\\ Frequency& 5& 11& 12& 13& 9\end{array}$$

• A. 50
• B. 110
• C. 55
• D. 100

Answer 1

The correct option is C 55

$$\begin{array}{ccc}ClassInterval& Frequency& CumulativeFrequency\\ 0-20& 5& 5\\ 20-40& 11& 16\\ 40-60& 12& 28\\ 60-80& 13& 41\\ 80-100& 9& 50\end{array}$$

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 28. The class corresponding to this frequency is 40-60. This is the median class.

Median = 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
$⟹Median=40+\frac{25-16}{20}\times 20=55$