Question

Question 16
The maximum bowling speeds, in km per hour, of 33 players at a cricket coaching centre are given as follow ?
$\begin{array}{ccccc}Speed\left(inkm/h\right)& 85-100& 100-115& 115-130& 130-145\\ Numberofplayers& 11& 9& 8& 5\end{array}$
Calculate the median bowling speed.

Answer 1

First we construct the cumulative frequency table
$\begin{array}{ccc}Speed\left(inkm/h\right)& Numberofplayers& Cumulativefrequency\\ 85-100& 11& 11\\ 100-115& 9& 11+9=20\\ 115-130& 8& 20+8=28\\ 130-145& 5& 28+5=33\end{array}$
It is given that n = 33
$\therefore \frac{n}{2}=\frac{33}{2}=16.5$
So, the median class is 100-115.
where, Lower limit (l) = 100,
frequency (f) = 9,
cumulative frequency preceding to median class ($c_f$)= 11
and class width(h) = 15
$\therefore$ $Median=l+\frac{(\frac{n}{2}-c_f)}{f}\times h$
$=100+\frac{(16.5-11)}{9}\times 15$
$=100+\frac{5.5\times 15}{9}=100+\frac{82.5}{9}=100+9.17$
$=109.17$
Hence, the median bowling speed is 109.17 km/h.