Question:
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.
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