Maintenance script: Initial automated import

2016-02-24T18:04:29Z

Initial automated import

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{{Template:TI-BASIC:Command
|picture=VARIANCE.GIF
|summary=Finds the sample variance of a list.
|syntax=variance(''list'',[''freqlist''])
|location=Press:
# 2ND LIST to enter the LIST menu.
# LEFT to enter the MATH submenu.
# 8 to select variance(, or use arrows.
|compatibility=TI-83/84/+/SE
|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.

= Formulas =

The formula for variance used by this command is:

{{Template:TI-BASIC:Math
|eqn = 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:

{{Template:TI-BASIC:Math
|eqn = \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 ''w,,i,,'', the formula becomes

{{Template:TI-BASIC:Math
|eqn = s_n^2 = \frac{\sum_{i=1}^N w_i(x_i - \overline{x})^2}{\sum_{i=1}^N (w_i)-1}
}}

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

= Related Commands =

* [[TI-BASIC:Mean|Mean(]]
* [[TI-BASIC:Median|Median(]]
* [[TI-BASIC:Stddev|StdDev(]][[Category:TI-BASIC]]
[[Category:TIBD]]

TI-BASIC:Variance - Revision history

Maintenance script: Initial automated import