Question

The maximum bowling speeds (in km/h) of 33 players at a cricket coaching centre are given below:

Speed in km/h	85-100	100-115	115-130	130-145
No. of players	10	4	7	9

Calculate the median bowling speed.

Answer 1

Speed (km/h)	No. of players $\left(f_i\right)$	c.f
85-100	10	10
100-115	4	14
115-130	7	21
130-145	9	30

N =30
$\therefore \frac{N}{2}=15$
The cumulative frequency just greater than 15 is 21.
$\therefore \mathrm{Median}\mathrm{Class}=115-130$
$\mathrm{i}.\mathrm{e}.,{\mathrm{x}}_{\mathrm{k}}=115,\mathrm{h}=15,\mathrm{f}=7,\mathrm{c}=\mathrm{c}.\mathrm{f}\mathrm{of}\mathrm{the}\mathrm{preceeding}\mathrm{class}=14,\frac{\mathrm{N}}{2}=15$
$$\begin{gathered} \therefore M_e=x_k+\left\{h\times \frac{\left(\frac{N}{2}-c\right)}{f}\right\} \\ =115+\left(15\times \frac{15-14}{7}\right) \\ =115+2.1 \\ =117.1 \end{gathered}$$
Hence, the required speed is 117.1 km/h.