In the provided dataset, the mean equals the median.

In the provided dataset, the mean equals the median.

• A. True
• B. False
• C. Not determinable
• D. Depends on distribution

Answer: (A)

Symmetry in data leads to equality of mean and median. The mean takes every value, adds them up, and divides by how many points there are, while the median is the middle value that splits the data into two equal halves. When the data are perfectly symmetric around a central value, every data point above the center has a mirror below it. Those mirrored pairs pull the mean toward the center just as the central position of the median sits at the center. As a result, both measures land on the same central value. In the dataset described, the data are arranged so that this symmetry holds, so the mean and the median coincide. For contrast, with skewed data (where one tail is longer or heavier), the mean shifts toward the tail while the median stays near the center, and they would not be equal. An example to visualize this is a symmetric set like -2, -1, 0, 1, 2, which has both mean and median equal to 0.

Symmetry in data leads to equality of mean and median. The mean takes every value, adds them up, and divides by how many points there are, while the median is the middle value that splits the data into two equal halves. When the data are perfectly symmetric around a central value, every data point above the center has a mirror below it. Those mirrored pairs pull the mean toward the center just as the central position of the median sits at the center. As a result, both measures land on the same central value.

In the dataset described, the data are arranged so that this symmetry holds, so the mean and the median coincide. For contrast, with skewed data (where one tail is longer or heavier), the mean shifts toward the tail while the median stays near the center, and they would not be equal. An example to visualize this is a symmetric set like -2, -1, 0, 1, 2, which has both mean and median equal to 0.