Which distribution shape results in the mean being greater than the median?

In the case of a skewed right distribution, the tail on the right side of the distribution is longer or fatter than the left side. This unevenness results in the mean being pulled in the direction of the tail, leading to a situation where the mean is greater than the median. The median, being the middle value when the data is ordered, remains more resistant to the influence of extreme values compared to the mean, which calculates the average of all values. Therefore, in a skewed right distribution, we typically observe that the mean is higher than the median due to these extreme higher values affecting the mean more significantly.

In contrast, other distribution types, like skewed left, symmetric, or normal distributions, feature different relationships between the mean and median, with skewed left typically resulting in the mean being less than the median, and symmetric or normal distributions yielding equal mean and median values.