Standard Deviation Calculator
Standard Deviation Lesson
What is the Standard Deviation?
In statistics, the standard deviation is a measure of how dispersed the values in a data set are. It is the square root of the variance. The formula for population standard deviation is given as:
And the formula for sample standard deviation is given as:
Where N is the number of values in the data set, xi is the data point of index i, μ is the population mean, and x̄ is the sample mean.
Why we Calculate the Standard Deviation of a Data Set
A large standard deviation means the values are very dispersed, on average the difference between values is large. A small standard deviation means the values are not very dispersed and have small differences between them on average.
We can create a distribution chart based on the dispersion of a data set. For example, we use the standard deviation to validate if a data set is normally distributed. A set is normally distributed if most of the data falls within 1, 2, and 3 standard deviations of the mean (see empirical rule).
How the Calculator Works
When you click the “calculate” button, the inputted data set gets formatted into a JS array. That array is then fed to a library of math functions, where the actual standard deviation calculation is performed. After rounding the answer, the standard deviation is printed to the output area in the calculator.