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Standard Deviation Calculator

Standard Deviation Calculator

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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 (s2) is the sum of the squared differences between each data point and the mean, divided by the number of data points (n) minus 1:

Variance = \( s^2 = \dfrac{\Sigma (x_{i} - \overline{x})^2}{n-1} \)

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

The total of all data values.
(x1 + x2 + x3 + ... + xn)
Count (n)
The total number of data values in a data set.
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 = s2
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 ]
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.

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