The Standard Deviation (SD or `sigma`) is a most common measure of variability in population or a data set. The standard deviation is used to quantify the amount of variation or dispersion of a set of data values.

What does the standard deviation tell us?

A low standard deviation indicates that the data points tend to be close to the mean.  

A high standard deviation indicates that the data is spread over a wider range of values.

The Math of the Standard Deviation

The standard deviation of a data set or statistical population is the square root of its variance. The standard deviation, unlike the variance, is expressed in the same units as the data.

The standard deviation (`sigma`)  is expressed here as the population SD:

`sigma = sqrt(sum_(i=1)^N(X_i - barX)N)`

This means we are calculating the SD on the whole of the data set, the whole population.

See Also

• Try the Mean calculation
• Try the Median calculation
• Try the Mode calculation
• Here's the Range of a data set
• Here's the Min calculation
• And the Max calculation
• Standard Deviation (Sample)
• Standard Deviation (Population)
• Frequency Distribution between min and max
• Frequency Distribution for population
• Try the z-score calculation on your data set
• Try the z-score when you know both mean and SD