# 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

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.

Expert Solution
Step 1

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.

Step 2

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.

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Follow-up Question

Suppose another researcher takes a random sample of 1000 subjects from the same population (US physicians who received payments from any of 8 major pharmaceutical companies in 2011). You have not yet seen these data. Likely, how will the sample standard deviation of these 1000 values (s1000) compare to the sample standard deviation of individual physician payments in the sample of 400 (s400=17 )

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