Explanation
Correct answer: C.
Choice C is correct. If the values in a data set are ordered from least to greatest, the median of the data set will be the middle value. Since each data set in the choices is ordered and contains exactly data values, the th value in each is the median. It follows that the median of the data set in choice C is . The sum of the positive differences between and each of the values that are less than is significantly smaller than the sum of the positive differences between and each of the values that are greater than . If were the mean, these sums would have been equal to each other. Therefore, the mean of this data set must be greater than . This can also be confirmed by calculating the mean as the sum of the values divided by the number of values in the data set: .
Desmos solution:
Note: The mean and median for each data set are computed directly using Desmos’s built-in functions. Only choice C shows a mean (113.56) greater than its median (32).
Enter in Desmos:
Reviewed and rewritten by CookSAT
Why the other choices are wrong
Choice A
Choice A is incorrect. The data set in this choice is symmetric with respect to its median, so the mean and the median for this choice are equivalent.
Choice B
Choice B is incorrect. The data set in this choice is symmetric with respect to its median, so the mean and the median for this choice are equivalent.
Choice D
Choice D is incorrect. The median of this data set is . Since the sum of the positive differences between and each of the values less than is greater than the sum of the positive differences between and each value greater than in this data set, the mean must be less than the median.