The population standard deviation, the standard definition of σ, is used when an entire population can be measured, and is the square root of the variance of a given data set. The calculator above computes population standard deviation and sample standard deviation, as well as confidence interval approximations. When used in this manner, standard deviation is often called the standard error of the mean, or standard error of the estimate with regard to a mean. In addition to expressing population variability, the standard deviation is also often used to measure statistical results such as the margin of error.
Similar to other mathematical and statistical concepts, there are many different situations in which standard deviation can be used, and thus many different equations. Conversely, a higher standard deviation indicates a wider range of values.
The lower the standard deviation, the closer the data points tend to be to the mean (or expected value), μ. Standard deviation in statistics, typically denoted by σ, is a measure of variation or dispersion (refers to a distribution's extent of stretching or squeezing) between values in a set of data.
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