Question

The maximum bowling speeds, in km per hour, 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 bowling speed.

Answer 1

First we construct the cumulative frequency table

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

∴ `n/2 = 33/2 = 16.5`

So, the median class is 100 – 115.

Where, lower limit (l) = 100,

Frequency (f) = 9,

Cumulative frequency (cf) = 11

And class width (h) = 15

∴ Median = `l + ((n /2 - cf))/f xx h`

= `100 + ((16.5 - 11))/9 xx 15`

= `100 + (5.5 xx 15)/9`

= `100 + 82.5/9`

= 100 + 9.17

= 109.17

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