When the Bell Curve Leans
Not all data distributions are symmetric. Skewness measures the direction and degree of asymmetry in a distribution.
A positively (right) skewed distribution has a long tail stretching toward higher values, like household income. A negatively (left) skewed distribution has a long tail toward lower values, like retirement age.
| Skew direction | Tail points | Mean vs. median |
|---|---|---|
| Positive (right) skew | Toward higher values | Mean > median |
| Negative (left) skew | Toward lower values | Mean < median |
| No skew (symmetric) | No tail | Mean = median |
Common pitfall: Skew is always named for where the tail points, not where the bulk of the data sits. A positively skewed distribution has most of its data on the left.
Skew and Central Tendency
Skew directly affects summary statistics. The mean is pulled toward the tail by extreme values, while the median remains stable.
For skewed data, the median better represents the typical case. Kurtosis is a separate property that describes how sharply peaked or flat a distribution is, independent of its skew.
Always check your distribution's shape before choosing whether to report the mean or the median.