Question

The distribution below gives the weights of $30$ students of a class. Find the median weight of the students.

$\begin{array}{cccccccc}\text{Weight(in Kgs)}& 40-45& 45-50& 50-55& 55-60& 60-65& 65-70& 70-75\\ \text{Number of students}& 2& 3& 8& 6& 6& 3& 2\end{array}$

Answer 1

$\begin{array}{cccccccc}\text{Weight(in Kgs)}& 40-45& 45-50& 50-55& 55-60& 60-65& 65-70& 70-75\\ \text{Number of students}& 2& 3& 8& 6& 6& 3& 2\\ \text{cumulative frequency}& 2& 5& 13& 19& 25& 28& 30\end{array}$
Here, $\frac{N}{2}=15$

So, the median class $=55-60$

Median $=L+\frac{(\frac{N}{2}-c)\times h}{f}$

here, $L=55,c=13,h=5,f=19$

Median $=55+\frac{(15-13)\times 5}{19}$

$=55+\frac{10}{19}$

$=55+0.526$

$=55.526$