Question:
The maximum bowling speeds, in km per hour, of 33 players at a cricket coaching centre are given as follows
Caluculate the median bowling speed.
Solution:
First we construct the cumulative frequency table
It is given that, $n=33$
$\therefore$ $\frac{n}{2}=\frac{33}{2}=16.5$
So, the median class is $100-115$.
where, $\quad$ lower limit $(l)=100$,
frequency $(t)=9$,
cumulative frequency $(c f)=11$
and $\quad$ class width $(h)=15$
$\therefore$ Median $=l+\frac{\left(\frac{n}{2}-c f\right)}{f} \times h$
$=100+\frac{(16.5-11)}{9} \times 15$
$=100+\frac{5.5 \times 15}{9}=100+\frac{82.5}{9}=100+9.17$
$=109.17$
Hence, the median bowling speed is 109.17 km/h.