Question

The maximum bowling speeds, in $kmperhour,$, of $33$ players at a cricket coaching centre are given as follows: Speed $(km/h)85-100,100-115,115-130,130-145$ Number of players $11,9,8,5$. Calculate the median of bowling speed.

Answer 1

Let us construct the cumulative frequency table at first

Speed ( in km/h)	Number of players	Cumulative frequency
85 – 100	11	11
100 – 115	9	11 + 9 = 20
115 – 130	8	20 + 8 = 28
130 – 145	5	28 + 5 = 33

It is given that, $n=33$

∴ $\frac{n}{2}=\frac{33}{2}=16.5$

Hence, the median class is $100-115$

Where, lower limit $\left(l\right)=100$

Frequency $\left(f\right)=9$

Cumulative frequency $\left(cf\right)=11$

And class width $\left(h\right)=15$

Median=$\begin{array}{l}l+\frac{\frac{n}{2}-c_f}{f}\times h\end{array}$

$$\begin{gathered} =100+\frac{16.5-11}{9}\times 15 \\ =100+\frac{82.5}{9} \\ =100+9.17 \\ =109.17 \end{gathered}$$

Hence, the median bowling speed is $109.17km/h$