# Standard Deviation Calculator

## Calculator Use

Standard deviation is a statistical measure of diversity or variability in a data set. A low standard deviation indicates that data points are generally close to the mean or the average value. A high standard deviation indicates greater variability in data points, or higher dispersion from the mean.

Enter a data set up to 5000 data points, separated by spaces, commas or line breaks. You can copy and paste your data from a text document or a spreadsheet. Click Calculate to find standard deviation, variance, count of data points (n), mean and sum of squares.

## Standard Deviation Formula

Standard deviation is the square root of the calculated variance of a set of data.

The formula for variance (s^{2}) is the sum of the squared differences between each data point and the mean, divided by the number of data points (n) minus 1:

Standard deviation = \( \sqrt {s^2} \)

For additional explanation of standard deviation and how it relates to a sample bell curve distribution, see Wikipedia's page on Standard deviation.

## Statistics Formulas and Calculations Used by This Calculator

- Sum
- The total of all data values.

(x_{1}+ x_{2}+ x_{3}+ ... + x_{n}) - Count (n)
- The total number of data values in a data set.
- Mean
- The sum of all of the data divided by the count; the average;

*mean = sum / n*. - Standard Deviation (s)
- The square root of the variance;

^{2}√variance or variance = s^{2} - Variance
- The sum of the squared differences between each data value and the mean, divided by the count (n) - 1;

[ (x1 - mean)^{2}+ (x2 - mean)^{2}+ (x3 - mean)^{2}+ ... + (xn - mean)^{2}] / [n - 1] - Sum of Squares
- The sum of the squared differences between data values and the mean;

[ (x1 - mean)^{2}+ (x2 - mean)^{2}+ (x3 - mean)^{2}+ ... + (xn - mean)^{2}] - Frequency
- The number of occurrences for each data value in the data set.

**Cite this content, page or calculator as:**

Furey, Edward "Standard Deviation Calculator"; from *http://www.calculatorsoup.com* - Online Calculator Resource.