Standard Deviation Calculator
Online calculator for the standard deviation of a data series
On this page the standard deviation of a series of numbers is calculated.
The standard deviation indicates the spread of the values around the mean value (arithmetic mean). The standard deviation is calculated using the square root of the variance
The standard deviation can be determined as the sample standard deviation for a partial quantity or for the total quantity. Different formulas apply to the total quantity or the sample.
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
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Standard deviation formula
Calculation of the standard deviation of a sample
\(\displaystyle s=\sqrt{ \frac{1}{n-1} \sum^n_{i=1} (x_i-\overline{x})^2} \)
\(s\) Standard deviation \(n\) Number of data points \(x_i\) Single data point \(\overline{x}\) Mean of the sample
Calculation of the standard deviation of a total quantity
\(\displaystyle σ=\sqrt{ \frac{1}{n} \sum^n_{i=1} (x_i-µ)^2} \)
\(σ\) Standard deviation \(n\) Number of data points \(x_i\) Single data point \(µ\) Mean of all data points
Example to the standard deviation of a sample
Daten \( \displaystyle x= 3, 5, 7, 8 \)
Mittelwert \( \displaystyle \overline{x}= \frac{3+ 5+ 7+ 8}{4} =5.75\)
\( \displaystyle s=\sqrt{\frac{1}{4-1}\cdot((3-5.75)^2+(5-5.75)^2+(7-5.75)^2+(8-5.75)^2)}\)
\( \displaystyle s=\sqrt{\frac{1}{3}\cdot(7.5625+0.5625+1.5625+5.0625)}\)
\( \displaystyle s=\sqrt{\frac{1}{3}\cdot 14.75} =\sqrt{ 4.9167}=\color{blue}{2.2174}\)
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
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