Skewness Calculator

Measure the asymmetry of a distribution and what it implies for analysis.

About Skewness Calculator

When the mean exceeds the median the distribution has a long right tail. Skewness beyond about one in absolute value usually means the mean is a poor summary and the median should be reported instead. Income and house-price data are strongly right-skewed, which is why medians rather than means are quoted in official statistics.

Formula

Skewness

Pearson’s second skewness coefficient = 3(mean − median) ÷ standard deviation

positive skew: Mean above median, a long right tail
standard error: √(6/n), used to judge whether the skew is meaningful

Worked example

With the default values below, Skewness Calculator returns Skewness of 1.00000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Mean: 52
Median: 48
Standard deviationminimum 0: 12
Sample sizeminimum 3: 200

Results

Skewness: 1.00000
Direction of Skew: Positively skewed — a long right tail
Severity: Severe
Standard Error of Skewness: 0.17321
Is the Skew Statistically Notable: Yes — the skew exceeds twice its standard error

Step by step

1Values used
2Skewness
3Skewness= 1.00000
4Direction of Skew= Positively skewed — a long right tail
5Severity= Severe
6Standard Error of Skewness= 0.17321
7Is the Skew Statistically Notable= Yes — the skew exceeds twice its standard error

Assumptions and limits

The result is derived only from the 4 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 5 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Skewness calculated?

Pearson’s second skewness coefficient = 3(mean − median) ÷ standard deviation When the mean exceeds the median the distribution has a long right tail. Skewness beyond about one in absolute value usually means the mean is a poor summary and the median should be reported instead.

Why does Skewness matter?

Income and house-price data are strongly right-skewed, which is why medians rather than means are quoted in official statistics.

What values do I need to enter?

This calculator takes 4 inputs: Mean, Median, Standard deviation, Sample size. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.