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.

What is the average age of the bears at your zoo? What is the standard deviation? Round your answers to the nearest tenth.

Khan AcademySign up

Practice calculating sample standard deviationA teacher weighed the backpacks of 4 students. Here are the weights (in kilograms):

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, …

Standard deviation measures how far apart numbers are in a data set. Variance, on the other hand, gives an actual value to how much the numbers in a data set vary from the mean.

Thus the sample standard error (standard deviation of the sample divided by the square root of n) is the statistic we are going to be using for calculating confidence intervals, and presumably …

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.

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

The population standard deviation is a measure of how much variation there is among individual data points in a population. It's a way of quantifying how spread out the data is from its mean.