Types of Skewness: Positive and Negative

A skewed distribution is classified by which tail is longer.

Positively skewed distribution — the right tail (higher values) is longer and thinner; most observations are concentrated at the lower end, with a few unusually large values pulling the tail to the right. In this case:

Negatively skewed distribution — the left tail (lower values) is longer and thinner; most observations are concentrated at the higher end, with a few unusually small values pulling the tail to the left. Here the order reverses:

<!-- FIGURE-NEEDED: Three frequency curves side by side on the same axes style — (1) a symmetric bell-shaped curve with Mean=Median=Mode marked at the single central peak; (2) a positively skewed curve (peak shifted left, long tail to the right) with Mode, Median, Mean marked left-to-right on the x-axis; (3) a negatively skewed curve (peak shifted right, long tail to the left) with Mean, Median, Mode marked left-to-right on the x-axis -->

Why the order of mean, median and mode reverses. The mean is the most sensitive of the three to extreme values, because every observation (however extreme) enters its calculation directly. The mode, by contrast, is entirely unaffected by extreme values — it only reflects where observations are most concentrated. The median sits between the two because it depends only on the position of the middle observation(s), not on how far the extreme values stretch. So when a few very large values are present (a long right tail), they pull the mean up the most, the median up a little, and leave the mode untouched — giving Mean > Median > Mode. The mirror argument gives Mean < Median < Mode for a long left tail. …