The maximum bowling speeds (in km/hr) of 33 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.
To find median, Assume
Σfi = N = Sum of frequencies,
h = length of median class,
l = lower boundary of the median class,
f = frequency of median class
and Cf = cumulative frequency
Lets form a table.
SPEED(in km/hr) | NUMBER OF PLAYERS(fi) | Cf |
85 - 100 | 10 | 10 |
100 - 115 | 4 | 10 + 4 = 14 |
115 - 130 | 7 | 14 + 7 = 21 |
130 - 145 | 9 | 21 + 9 = 30 |
TOTAL | 30 |
So, N = 30
⇒ N/2 = 30/2 = 15
The cumulative frequency just greater than (N/2 = ) 15 is 21, so the corresponding median class is 115 - 130 and accordingly we get Cf = 14(cumulative frequency before the median class).
Now, since median class is 115 - 130.
∴ l = 115, h = 15, f = 7, N/2 = 15 and Cf = 14
Median is given by,
⇒ 
= 115 + 2.14
= 117.14
Thus, median is 117.14 km/hr.