Question

Calculate the median for the following distribution.

$\begin{array}{cc}Marksobtained& Numberofstudents\\ Below10& 6\\ Below20& 15\\ Below30& 29\\ Below40& 41\\ Below50& 60\\ Below60& 70\end{array}$

Answer 1

The frequency distribution table from the given distribution is as follows:

$\begin{array}{ccc}Class& Numberof& Cumulative\\ \left(Marksobtained\right)& students& frequency\\ & \left(frequency\right)& \\ 0-10& 6& 6\\ 10-20& 9& 15\\ 20-30& 14& 29\\ 30-40& 12& 41\\ 40-50& 19& 60\\ 50-60& 10& 70\end{array}$

n = 70 $\therefore \frac{n}{2}=35$. This observation lies in the class 30 - 40. So, 30 - 40 is the median class.

$\therefore$ l = 30, h = 10, cf = 29, f = 12

Using the formula, Median $=l+\left(\frac{\frac{n}{2}-cf}{f}\right)\times h$, we get

Median $=30+\left(\frac{35-29}{12}\right)\times 10=30+5=35$