Standard deviation

Standard deviation is one of the most widely used measures of dispersion in statistics. It shows how spread out the data is from the mean, and can be calculated for both populations and samples.

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The standard deviation measures the dispersion of the values of a dataset with respect to its mean. It is calculated using the formula:

Population standard deviation formula

If it is a sample, the following formula is used:

Sample standard deviation formula

where:

  • x_i are the values of the dataset.
  • vec{x} is the mean of the dataset.
  • n is the total number of observations.
  • σ is the population standard deviation (when we have the entire population data).
  • s is the sample standard deviation (when we have a sample and want to estimate the population’s dispersion).

  • See Calculation in Python
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