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If a data set contains the numbers 5, 8, 10, 12, and 15, which of the following statements about the data set is true?

Rationale

The median is equal to the mean.

In the given data set (5, 8, 10, 12, 15), both the mean and the median equal 10, making this statement true. This equality occurs because the data set is symmetric, with an evenly distributed set of numbers.

A (The median is greater than the mean.) YOUR ANSWER

This statement is incorrect because both the median and the mean are equal to 10 in this data set. Therefore, the median cannot be greater than the mean, as they are the same value.

B (The range is less than the median.) YOUR ANSWER

The range of the data set is calculated by subtracting the smallest value (5) from the largest value (15), resulting in a range of 10. Since the median is also 10, the range is not less than the median, making this statement false.

C (The median is equal to the mean.) CORRECT

As previously established, the median of the data set is 10 (the middle value), and the mean is also calculated to be 10 (the sum of the values divided by the number of values). Thus, this statement is true.

D (The mean is greater than the median.) YOUR ANSWER

Given that both the mean and the median are equal to 10, this statement is false. The mean cannot be greater than the median when they are identical.

Conclusion

In this data set, the mean and median are both equal to 10, confirming that they match each other exactly. This equality highlights a symmetric distribution of the numbers, which is a key characteristic in statistical analysis. Therefore, the only accurate statement from the options provided is that the median is equal to the mean.

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