# Standard Deviation (SD)

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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  of the data set, that the data adheres to the central tendency to be close to the mean and not to vary wildly from 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.