Variance Calculator

The variance refers to a statistical measurement of the spread between numbers in a data set. So the variance measures how far each number in the set is from the mean.

The variance can be determined as the sample variance for a subset or for the entire set. Different formulas apply to the total quantity or the sample.

To perform the calculation, enter a series of numbers. Then click the 'Calculate' button.

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

Variance formulas

Empirische Varianz

Calculating the variance of a sample

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

\(s^2\)	Variance
\(n\)	Number of data points
\(x_i\)	Single data point
\(\overline{x}\)	Mean of the sample

Calculation of the variance of a total quantity

\(\displaystyle σ^2=\frac{1}{n} \sum^n_{i=1} (x_i-µ)^2 \)

\(σ\)	Variance
\(n\)	Number of data points
\(x_i\)	Single data point
\(µ\)	Mean of all data points

Example for the variance of a sample

data set \( \displaystyle x= 3, 5, 7, 8 \)

mean \( \displaystyle \overline{x}= \frac{3+ 5+ 7+ 8}{4} =5.75\)

\( \displaystyle s^2=\frac{1}{4-1}\cdot((3-5.75)^2+(5-5.75)^2+(7-5.75)^2+(8-5.75)^2)\)

\( \displaystyle s^2=\frac{1}{3}\cdot(7.5625+0.5625+1.5625+5.0625)\)

\( \displaystyle s^2=\frac{1}{3}\cdot 14.75 =\color{blue}{4.9167}\)

More statistics functions

Arithmetic Mean • Contraharmonic Mean • Covariance • Empirical distribution CDF • Deviation • Five-Number Summary • Geometric Mean • Harmonic Mean • Inverse Empirical distribution CDF • Kurtosis • Log Geometric Mean • Lower Quartile • Median • Pooled Standard Deviation • Pooled Variance • Skewness (Statistische Schiefe) • Upper Quartile • Variance