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Question

25 athletes participate in a race and all of them finish it. The distribution of times taken to complete the race by athletes (in minutes) is shown in the table below. Calculate the mean of the finish times taken by the given population of athletes.

Finish time
(minutes)
0 to less than 1(0
10 to less than 20
20 to less than 30
30 to less than 40
40 to less than 50
Numberof
athletes
3
10
6
4
2
Transcribed Image Text

Finish time (minutes) 0 to less than 1(0 10 to less than 20 20 to less than 30 30 to less than 40 40 to less than 50 Numberof athletes 3 10 6 4 2

Expert Answer

This is a problem on finding the mean of continuous grouped data. We first find the midpoint of each interval. For example, the first interval or class is 0 - 10. The mid-point of this class will be (0 + 10)/2 = 5.

We now calculate the product of mid-point and frequency for each class. Here, the number of athletes in each class is the frequency of that class. For example, for the first class 0 – 10, its frequency is 3.

We can now use the formula to calculate mean. Note that the number of athletes is N = 25.

Answer: The mean for the given distribution of finish times in a race is 21.8 minutes.