Definition · Plain-language
Skewness
Skewness is a measure of the asymmetry of a distribution — the extent to which it leans to one side rather than being symmetric around its centre.
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Asymmetry of a distribution
Skewness describes how lopsided a distribution is. A perfectly symmetric distribution, such as the normal curve, looks the same on both sides of its centre and has a skewness of zero. When one tail is longer or fatter than the other, the distribution is skewed, and skewness quantifies the degree and direction of that imbalance. The direction is named after the side on which the long tail lies, not the side where the bulk of the data sits — a convention that catches many people out. Skewness is one of the basic shape characteristics of a distribution, alongside its centre and spread.
Positive (right) and negative (left) skew
In a positively skewed, or right-skewed, distribution the long tail extends towards the higher values on the right, while most observations cluster at the lower end. Income is a classic example: most people earn modest amounts and a few earn very large sums, stretching the right tail. In a negatively skewed, or left-skewed, distribution the long tail extends towards the lower values on the left, with most observations bunched at the higher end — for instance, ages at death in a developed country, where most deaths occur in old age and a few occur much younger. The sign of the skewness statistic matches the side of the long tail.
Effect on the mean and median
Skew has a predictable effect on the relationship between the mean and the median. The mean is sensitive to extreme values, so the long tail drags it in the direction of the skew, whereas the median, being the middle value, is far less affected. In a right-skewed distribution the mean is therefore typically greater than the median; in a left-skewed distribution the mean is typically less than the median; and in a symmetric distribution the two roughly coincide. This is why, for noticeably skewed data such as incomes or house prices, the median is usually the more representative measure of a typical value than the mean.
Key facts
At a glance
- Definition: a measure of the asymmetry of a distribution
- Symmetric: a symmetric distribution has zero skewness
- Positive skew: long tail to the right; most data on the left
- Negative skew: long tail to the left; most data on the right
- Naming: skew is named for the side of the long tail
- Effect: the long tail pulls the mean towards it, away from the median
Common misconceptions
What people often get wrong
Often heard: A right-skewed distribution is called that because most of its data sit on the right.
Actually: Skew is named for the long tail, not the bulk of the data. In right (positive) skew most values cluster on the left, and the thin tail stretches to the right.
Often heard: Skewness changes the spread of a distribution but not its mean.
Actually: Skew pulls the mean towards the long tail, so in a right-skewed distribution the mean usually exceeds the median, and in a left-skewed one it falls below it.
Often heard: A skewness value of zero guarantees a normal distribution.
Actually: Zero skewness means symmetry, not normality. Other symmetric distributions, and some non-normal ones, also have zero skew; normality requires more than the absence of skew.
