Calculate the median from the following data:

Solution:

First we prepare the following cummulative table to compute the median.

Here, $N=140$

So, $\frac{N}{2}=70$

Thus, the cumulative frequency just greater than 70 is 98 and the corresponding class is $55-65$.

Therefore, $55-65$ is the median class.

Here, $l=55, f=40, F=58$ and $h=10$

We know that

Median $=l+\left\{\frac{\frac{N}{2}-F}{f}\right\} \times h$

$=55+\left\{\frac{70-58}{40}\right\} \times 10$

$=55+\frac{12 \times 10}{40}$

$=55+\frac{120}{40}$

$=55+3$

 

$=58$

Hence, the median is 58.