In the table given below, the times taken by 120 athletes to run a 100 - m - hurdle race are given.
Class | 13.8 - 14 | 14 - 14.2 | 14.2 - 14.4 | 14.4 - 14.6 | 14.6 - 14.8 | 14.8 - 15 |
Frequency | 2 | 4 | 15 | 54 | 25 | 20 |
Find the number of athletes who completed the race in less than 14.6 seconds.
We need to form a ‘less than type’ table to solve this.
CLASS | FREQUENCY | CUMULATIVE FREQUENCY (Cf) |
Less than 14 | 2 | 2 |
Less than 14.2 | 4 | 2 + 4 = 6 |
Less than 14.4 | 15 | 6 + 15 = 21 |
Less than 14.6 | 54 | 21 + 54 = 75 |
Less than 14.8 | 25 | 75 + 25 = 100 |
Less than 15 | 20 | 100 + 20 = 120 |
Here, cumulative frequency shows number of athletes taking different time intervals to run a 100 - m - hurdle race.
So by the table, there are 75 athletes who completed the race in less than 14.6 seconds.