Standard Deviation Calculator

A calculator to compute the standard deviation of a data set of real numbers x1, x2, x3 ... xN. The definition of the standard deviation of a population and a sample are as follows:
The standard deviation ? of a population having N elements is defined by
\sigma =\sqrt {\dfrac{\sum_{i=1}^{N} (x_i - \mu)^2}{N}}
\mu = \dfrac{\sum_{i=1}^{N} x_i}{N}

In some situations, when the data set is too large, we use samples of that set ( or population ) to estimate the standard deviation of the set. The standard deviation s of a sample having N data values is defined by
s =\sqrt {\dfrac{\sum_{i=1}^{N} (x_i - \overline{x})^2}{N - 1}}
\overline{x} = \dfrac{\sum_{i=1}^{N} x_i}{N}

Use Standard Deviation Calculator

Enter the list of real numbers x1, x2, x3 ... xN separated by commas, check the data entered and then press "Calculate Standard Deviation". The outputs are the population and sample standard deviations using the formulas above.
"NaN" means "not a number" and when it is displayed for a data value, check that data value and make corrections before any calculations.
Possible mistakes to avoid : extra space between digits, two successive commas, comma at the end of the list of the numbers entered, etc ....
If you have data values separated by commas and well formated, you may copy and paste them in the text area. The text area to input data can be made much larger by pulling its bottom right hand side.

Enter Data Values: x1, x2, x3 ... =
Decimal Places =

Check Entered Data: =
Population Standard Deviation: =
Sample Standard Deviation: =

More References and Links

standard deviation
Mean and Standard deviation.
Statistics Calculators, Solvers and Graphers.