Standard Deviation Formula

Standard Deviation



The standard deviation formula represents the distribution of the population data around the mean of the population. A smaller standard deviation means that most of the data is close to the mean. A bigger standard deviation means that the data is more spread out over the sample space.

Expression Description
The population standard deviation
The size of the population
Element of the population
Average value of the population

Usage Notes

This formula represents an approximation of the population standard deviation. Of course, as the size of the sample increases the closer the sample and population standard deviation become. The symbols μ (mu) and σ (sigma) are used to differentiate between the sample which a subset of the whole population.

Sample standard deviation.

The value for the standard deviation can be used to understand how closely the data set is to the mean. One standard deviation away from the mean on either side contains approximately 68.3% of the samples, two standard deviations contains approximately 95.4% of the samples, and so on.

Standard deviation area percentage.

Bessel’s Correction

Bessel’s Correction ensures that the value returned from the formula will conservatively estimate the standard deviation.