Skewness

Skewness measures the asymmetry of a distribution. Positive (right) skew shows a long upper tail with mean above median; negative (left) skew the reverse. A symmetric distribution has zero skewness.

ByHoang TruongUpdated June 30, 2026

See it move

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Positive (right) skew has a long upper tail, pulling the mean above the median above the mode — income data is the classic case, since a few very high earners stretch the average upward. Negative (left) skew reverses the order: a long lower tail pulls the mean below the median below the mode. A symmetric distribution has zero skewness and mean equal to median equal to mode.

Where it fits

TopicDescriptive StatisticsAdvancedSubjectData Analysis & StatisticsAdvanced

The formula

LaTeX

\text{Pearson's skewness coefficient} = \frac{3 \times (\text{Mean} - \text{Median})}{\text{Standard deviation}}

Variables

$M e an$: Arithmetic mean of the dataset
$M e d ian$: Middle value of the ordered dataset
$S t an d a r dd e v ia t i o n$: Sample standard deviation s

Positive result indicates right (positive) skew; negative indicates left (negative) skew; zero indicates symmetry.

Check yourself

PracticeCORE

An HR analyst finds that the mean annual bonus at a firm is €13,800 and the median annual bonus is €8,200. What do these figures suggest about the shape of the bonus distribution, and which measure better represents a typical employee's experience?

Select an answer to check your understanding.