Skewness

in statistics the skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. Negative skew commonly indicates that the tail is on the left side of the distribution, and positive skew indicates that the tail is on the right.

To perform the calculation, enter a series of numbers. Then click the 'Calculate' button. The list can be entered unsorted.

Input format

The data can be entered as a series of numbers, separated by semicolons or spaces. You can enter the data as a list (one value per line). Or from a column from Excel spreadsheet by copy & paste

Skewness Formula

The skewness of a sample is determined by the following formula:

\(\displaystyle g_m = \frac{1}{n} \sum^n_{i=1} \left( \frac{x_i - \overline{x}}{s}\right)^3 \)

The skewness of the total population is determined by the following formula:

\(\displaystyle G_m = \frac{n}{(n-1)(n-2)} \sum^n_{i=1} \left( \frac{x_i - \overline{x}}{s}\right)^3 \)

\(x_i\)  Single data point
\(\overline{x}\)   Arithmetic mean
\(s\)   Standard deviation
\(n\)   Number of data points