Which distribution shape typically results in the mean being less than the median?

In a skewed left distribution, also known as negatively skewed, the tail on the left side of the distribution is longer or fatter than the right side. This characteristic affects the position of the mean and median. Since the mean is influenced by extreme values in the dataset, a few lower values in the left tail will pull the mean downward, thereby making it less than the median, which is the middle value that is less affected by these extreme lower values.

In contrast, a skewed right distribution has a longer tail on the right side, which causes the mean to be greater than the median due to higher values affecting the mean calculation. A symmetric distribution has the mean and median equal because the values are evenly distributed on either side of the center. Finally, a uniform distribution features equal frequency across all values and also results in the mean being equal to the median. Therefore, in a skewed left distribution, it is clear how the placement of the mean relative to the median is affected by the shape and characteristics of the distribution.