Variance Calculator
Online calculator for calculating the variance of a data series
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
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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