Skewness and Kurtosis

Tap a term to see what it means, or .

Calculate

Example: the monthly income, in thousands, of fifteen families. Most earn little and a few earn a lot. How skewed is this distribution, and how heavy are its tails? Change the values to work out your own case.

Values x_i At least four, separated by spaces or commas.

Step by step

What each term means

Skewness (g₁): Positive when the long tail is on the right (rare, distant high values, like income); negative when it is on the left; near zero, symmetric. Kurtosis, g₂, similarly measures how heavy the tails are.
Third Moment: The mean of the cubed deviations. Cubing keeps the sign and magnifies large deviations, so the longer tail decides the result.
Standard Deviation Cubed: Divides the third moment by the scale of the data, raised to the same power: that way skewness has no unit and doesn't change whether the data are in dollars or thousands of dollars.