The variance( Command

Command Summary

Finds the sample variance of a list.

Command Syntax


Menu Location


  1. 2ND LIST to enter the LIST menu.
  2. LEFT to enter the MATH submenu.
  3. 8 to select variance(, or use arrows.

Calculator Compatibility


Token Size

1 byte

The variance( command finds the sample variance of a list, a measure of the spread of a distribution. It takes a list of real numbers as a parameter. For example:

:Prompt L1
:Disp "VARIANCE OF L1",variance(L1

Advanced Uses

Frequency lists don't need to be whole numbers. Amazing as that may sound, your calculator can handle being told that one element of the list occurs 1/3 of a time, and another occurs 22.7 times. It can even handle a frequency of 0 - it will just ignore that element, as though it weren't there. One caveat, though - if all of the elements occur 0 times, there's no elements actually in the list and your calculator will throw an error.


The formula for variance used by this command is:

\begin{align} s_n^2 = \frac{1}{N-1} \sum_{i=1}^N (x_i - \overline{x})^2 \end{align}

This is the formula for sample variance. The formula for population variance, which this command does not use, varies slightly:

\begin{align} \sigma^2 = \frac{1}{N} \sum_{i=1}^N (x_i - \overline{x})^2 \end{align}

If the population variance is required, just multiply the result of variance() by 1-1/N.

With frequencies wi, the formula becomes

\begin{align} s_n^2 = \frac{\sum_{i=1}^N w_i(x_i - \overline{x})^2}{\sum_{i=1}^N (w_i)-1} \end{align}

where $\definecolor{darkgreen}{rgb}{0.90,0.91,0.859}\pagecolor{darkgreen} \overline{x}$ is the mean with frequencies included.

Related Commands


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