When is the mean typically greater than the median in a skewed distribution?

In a right skewed distribution, the mean is typically greater than the median due to the presence of outliers or a tail extending towards the higher values. In this type of distribution, the bulk of the data points are concentrated on the left side, with a few extreme high values pulling the mean to the right. This results in the mean being disproportionately affected by these high values compared to the median, which is less sensitive to extreme outliers as it represents the middle value when the data is arranged in order.

For example, consider a dataset of incomes where most individuals earn between $30,000 to $50,000, but a small number earn much higher, such as $200,000. The mean income would be significantly raised by those high earners, whereas the median, representing the middle income, would stay closer to the average income within the majority, illustrating that in a right skewed distribution, it is common for the mean to exceed the median.

In contrast, left skewed distributions have the opposite relationship, with the mean being less than the median due to low values on the tail side skewing the mean downward. Symmetrical distributions and normal distributions, by definition, have the mean and median equal, as the data is evenly distributed