Question

The distribution below gives the weights of 30 students of a class. Find the median weight of the students.
$\begin{array}{cccccccc}Weight\left(inkg\right)& 40-45& 45-50& 50-55& 55-60& 60-65& 65-70& 70-75\\ Numberofstudents& 2& 3& 8& 6& 6& 3& 2\end{array}$

Answer 1

We may find the cumulative frequencies with their respective class intervals as below:
Cumulative frequency just greater than $\frac{n}{2}(i.e,\frac{30}{2}=15)$ is 19, belonging to class interval 55 - 60.
Median class = 55 - 60
Lower limit $l$ of median class = 55
Frequency $f$ of median class = 6
Cumulative frequency $cf$ of median class = 13
Class size $h$ = 5
$Median=l+\left(\frac{\frac{n}{2}-cf}{f}\right)\times h$
$=55+\left(\frac{15-13}{6}\right)\times 5$
$=55+\frac{10}{6}$
$=56.666$
So, median weight is 56.67 kg.