The finish times (in minutes) for runners in three-mile courses at Events A and

Question

The finish times (in minutes) for runners in three-mile courses at Events A and B are shown in the histogram below. At each event, the women's mean time was 19 minutes and the men's mean time was 17 minutes. At one event, the standard deviations for the women's times and the men's times were both 0.5 minute. At the other event, the standard deviations for the women's times and the men's times were both 2.5 minutes. Running Event A Running Event B 350 300 250 200 150 100 50 250 200 150 100 50 9 12 15 18 21 24 27 15 16 1718 19 20 21 Minutes Minutes At which event, A or B, were the standard deviations for women and men both 0.5 minutes? At which event, A or B, were the standard deviations for women and men both 2.5 minutes? Refer to the given means and standard deviations to explain why the distribution for Even A is mound shape symmetrical but the distribution for Event B is bimodal. When determining how different women's times are from men's times, explain why it is not enough to simply compare the mean times. 1. 2. 3. 4.

Explanation / Answer

1. At event B, the standard deviations for women and men both were 0.5 minutes.

Reason : Values are less dispersed for histogram of event B

2. At event A, the standard deviations for women and men both were 2.5 minutes.

Reason : Values are more dispersed for histogram of event A

3. The distribution for Event A is mound shape symmetrical because it is making a bell shape and it has only one peak , therefore it is unimodal.

The distribution for Event B is bimodal because it has two peaks and the distribution with two peaks is called bimodal.

4. It is not enough to simply compare the mean times because the standard deviation of times for Men and Women are not same for Event A and Event B. So we need to compare the standard deviations also.

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