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The variance( Command

Command Summary Command Syntax Calculator Compatibility Token Size
Finds the sample variance of a list. variance(list,[freqlist]) TI-83/84/+/SE 1 byte

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

The variance( Command

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.

Formulas

The formula for variance used by this command is:

\[ s_n^2 = \frac{1}{N-1} \sum_{i=1}^N (x_i - \overline{x})^2 \]

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

\[ \sigma^2 = \frac{1}{N} \sum_{i=1}^N (x_i - \overline{x})^2 \]

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

With frequencies wi, the formula becomes

\[ s_n^2 = \frac{\sum_{i=1}^N w_i(x_i - \overline{x})^2}{\sum_{i=1}^N (w_i)-1} \]

where \(\overline{x}\) is the mean with frequencies included.

Authors: KG