Decide whether the following statement makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. There's much more variation in the ages of the general population than in the ages of students in my college extension course, but both distributions have the same mean. Choose the correct answer below. A. The statement does not make sense because a college class could never have the same mean as the general population. B. The statement does not make sense because variation is based on the mean, so data sets with different variations cannot have the same mean. C. The statement makes sense because in order to compare the variation of two different data sets, they must have the same mean. D. The statement makes sense because two data sets can be spread out differently and still have the same mean.
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D. The statement makes sense because two data sets can be spread out differently and still have the same mean. Here's the reasoning: The mean is simply the average of a set of values, and it's possible for one group, like the general population, to have a wide range of ages while still having the same average age as a more narrowly defined group like college extension students. Variability, or how spread out values are, can differ without affecting the mean, allowing both groups to share the same average age despite their different age ranges.
