Statistics Calculator: Variance

Use this calculator to compute the variance from a set of numerical values.

Data is from: Population Sample

Variance Calculator Instructions

This calculator computes the variance from a data set:

To calculate the variance from a set of values, specify whether the data is for an entire population or from a sample. Enter the observed values in the box above. Values must be numeric and may be separated by commas, spaces or new-line. You may also copy and paste data into the text box. Press the "Submit Data" button to perform the computation. To clear the calculator and enter a new data set, press "Reset".

What is the variance

The variance is one of the measures of dispersion, that is a measure of by how much the values in the data set are likely to differ from the mean of the values. It is the average of the squares of the deviations from the mean. Squaring the deviations ensures that negative and positive deviations do not cancel each other out.

Variance formulas

This calculator uses the following formulas for calculating the variance:

The formula for the variance of a sample is:

$ s^2 ={\frac{1}{n-1} \sum_{i=1}^n (x_i-\bar{x})^2$

where n is the sample size and x-bar is the sample mean.

The formula for the variance of an entire population is:

$ \sigma^2 =\frac{1}{N} \sum_{i=1}^N (x_i-\mu)^2$

where N is the population size and μ is the population mean.

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