Question

The maximum bowling speed (km/hour) of 33 players at a cricket coaching centre is given below.

Bowling speed (km/hr)	85-100	100-115	115-130	130-145
No. of players	9	11	8	5

Find the modal bowling speed of the players.

Answer 1

Bowling speed (km/hr)	No. of players (Frequency)
85-100	$9\to f_1$
100-115	$11\to f_m$
115-130	$8\to f_2$
130-145	5

Here, the maximum frequency f_m is 11. So, the corresponding modal class is 100-115.
$$\begin{gathered} \mathrm{Mode}=L+\left[\frac{f_m-f_1}{2f_m-f_1-f_2}\right]h \\ \text{Here},L=\mathrm{lower}\mathrm{limit}\mathrm{of}\mathrm{the}\mathrm{modal}\mathrm{class}=100 \\ {f}_m=\mathrm{maximum}\mathrm{frequency}=11 \\ {f}_1=\mathrm{frequency}\mathrm{of}\mathrm{premodal}\mathrm{class}=9 \\ {f}_2=\mathrm{frequency}\mathrm{of}\mathrm{postmodal}\mathrm{class}=8 \\ h=\mathrm{width}\mathrm{of}\mathrm{modal}\mathrm{class}=15 \\ \therefore \mathrm{Mode}=100+\left[\frac{11-9}{2\left(11\right)-9-8}\right]\times 15 \\ =100+\left[\frac{2}{22-17}\right]\times 15 \\ =100+\frac{2}{5}\times 15 \\ =100+6=106 \\ \therefore \mathrm{The}\mathrm{modal}\mathrm{bowling}\mathrm{speed}\mathrm{of}\text{the}\mathrm{players}\mathrm{is}106\mathrm{km}/\mathrm{hour}. \end{gathered}$$