Question : A 110 m hurdle race is organised for a group of 150 athletes. The time in seconds, taken by the athletes to run the race are tabulate below :
|
Time (in Sec)
|
No. of Athletes
|
|
13.8-14.0
|
2
|
|
14.0-14.2
|
4
|
|
14.2-14.4
|
5
|
|
14.4-14.6
|
71
|
|
14.6-14.8
|
48
|
|
14.8-15.0
|
20
|
1. What is the class marks of the class interval corresponding to frequency 48?
2. Find the median time taken by an athlete to finish the race.
Solution :
1) Class Marks of the class interval corresponding to frequency 48 is given by
= (14.6+14.8)/2
= (29.4)/2
= 14.7
|
Time (in Sec)
|
No. of Athletes
|
Cumulative Frequency (CF) |
|
13.8-14.0
|
2
|
2 |
|
14.0-14.2
|
4
|
6 |
|
14.2-14.4
|
5
|
11 |
|
14.4-14.6
|
71
|
82 |
|
14.6-14.8
|
48
|
130 |
|
14.8-15.0
|
20
|
150 |
|
Total
|
150
|
Σfi = n = 150
n/2 = 150/2 = 75
Median Class = 14.4-14.6
Lower Limit (l) = 14.4
Class Size (h)
= (14.6-14.4)
= 0.2
= (14.6-14.4)
= 0.2
f = 71
CF = 11
CF = 11
= 14.58 sec
Hence, the median time taken by the an athlete to finish the race is 14.58 sec.