In a data set where the mean is 78 and the median is 80, what does this suggest about the distribution?

• A. The distribution is symmetric.
• B. The distribution is slightly left-skewed (tail toward lower values).
• C. The distribution is right-skewed (tail toward higher values).
• D. The data are all identical.

Answer: (B)

When the mean is less than the median, the distribution tends to be left-skewed (negatively skewed). The mean is pulled toward the tail with low values, while the median reflects the middle value and is less affected by extreme data points. Here, the mean is 78 and the median is 80, so the mean being slightly lower indicates a tail toward lower values, i.e., a mild left skew. If the data were symmetric, the mean and median would be about the same; a right-skew would have the mean higher than the median. All identical values would make both equal and yield no skew.