Question

The maximum bowling speeds (in km/hr) of 30 players at a cricket coaching centre are given below:

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

Calculate the median bowling speed.

Answer 1

1. Construct cumulative frequencies

To find the median for grouped data, first determine the cumulative frequency (cf) for each class interval by adding the frequencies sequentially:

Speed (in km/hr)	Number of players (f)	Cumulative frequency (cf)
85 – 100	10	10
100 – 115	4	10 + 4 = 14
115 – 130	7	14 + 7 = 21
130 – 145	9	21 + 9 = 30

The total number of observations is N = 30.

2. Identify median class

Find the value of `N/2`:

`N/2 = 30/2 = 15`

Look at the cumulative frequency column to find the first value greater than or equal to 15. That cumulative frequency is 21, which corresponds to the class interval 115 – 130.

Thus, the median class is 115 – 130.

3. Apply median formula

The formula to calculate the median for grouped data is:

Medain = `L + ((N/2 - cf)/f) xx h`

From our median class (115 – 130), extract the required values:

L (lower limit of the median class) = 115

cf (cumulative frequency of the preceding class) = 14

f (frequency of the median class) = 7

h (class width/size) = 130 – 115 = 15

Substitute these values into the formula:

Median = `115 + ((15 - 14)/7) xx 15`

Median = `15 + (1/7) xx 15`

Median = `115 + 15/7`

Median = 115 + 2.1428...

Median ≈ 117.14 km/hr

The calculated median bowling speed for the 30 cricket players is 117.14 km/hr.