A local swim club offers competitive meets throughout the season. Some races are

Question

A local swim club offers competitive meets throughout the season. Some races are open competitions with no qualifying times. Other races are qualified competitions. For example, 15- to 16-year-old girls are eligible to swim the 100-meter freestyle in a qualified competition if they posted a time of 1-minute 8-second time or less during the qualifying period.

Consider the group of 15- to 16-year-old females who swim the 100-meter freestyle in the open competitions and the group of 15- to 16-year-old females who swim the 100-meter freestyle in the qualified competitions. Which group’s distribution of race times would most likely have the largest standard deviation?

The group competing in the open competitions is most likely to have a higher standard deviation than the group competing in the qualified competitions.

The group competing in the qualified competitions is most likely to have a higher standard deviation than the group competing in the open competitions.

Both groups would likely have the same standard deviation.

There is not enough information to predict the relative sizes of their standard deviations.

Explanation / Answer

The group competing in the open competitions is most likely to have a higher standard deviation than the group competing in the qualified competitions. This is because there is a minimum time that has to be achieved to participate in the qualified competitions whereas there is no time limit to participate in the open competitions and thus, the standard deviation will be large.

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