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; 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.


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 $\overline{x}$ is the mean with frequencies included.

Related Commands


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