The formula we use for standard deviation depends on whether the data is being considered a population of its own, or the data is a sample representing a larger population.

A standard deviation close to 0 indicates that the data points tend to be close to the mean (shown by the dotted line). The further the data points are from the mean, the greater the standard deviation.

The standard deviation formula may look confusing, but it will make sense after we break it down. In the coming sections, we'll walk through a step-by-step interactive example.

Standard deviation involves adding and subtracting values at various steps in the calculation process. For example, the differences between each data point and the mean are calculated, squared, …

The formula we use for standard deviation depends on whether the data is being considered a population of its own, or the data is a sample representing a larger population.

Practice calculating and interpreting the mean and standard deviation of a discrete random variable.

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Sal shows an example of calculating standard deviation and bias. Created by Sal Khan.

Mean (expected value) of a discrete random variable Mean and standard deviation of a binomial random variable

Calculating standard deviation step by step Standard deviation of a population Mean and standard deviation versus median and IQR Concept check: Standard deviation Statistics: Alternate variance …