Using these formulas, we can conceptualize where we would expect the mean to fall on each type of distribution.

The graph is symmetric, with the median and mean both in the center.
Symmetric
Mean = Median = Mode
The graph is skewed to the right, with the median to the left of the mean.
Skewed Right
Mean > Median > Mode
The graph is skewed to the left, with the median to the right of the mean.
Skewed Left
Mean < Median < Mode

For a symmetric distribution, we would expect the mean to be roughly equal to the median and the mode, at the peak of the distribution. In a bell-shaped distribution, each value from the right side of the center of the distribution will be offset in the formula for the mean by a value equidistant from the center but on the left side of the center.

For a distribution skewed to the right, there are more values to the right of the distribution's peak than to the left. More importantly, there are some values that fall to the extreme right, and thus have a larger impact on the mean. The result is that the mean will be significantly larger than the median and the mode of the distribution.

The same holds true in the opposite direction for a left-skewed distribution. A larger number of more extreme values on the left side of the distribution will cause the mean to be significantly less than the median and the mode.

On the next screen, we will visualize the connection between distribution shape and the mean.