The variance( Command

Command Summary

Finds the sample variance of a list.

Command Syntax

variance(list,[freqlist])

Press:

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

TI-83/84/+/SE

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


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.

# Formulas

The formula for variance used by this command is:

(1)
\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:

(2)
\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

(3)
\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.

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