TI-BASIC:Variance

From Learn @ Cemetech
Revision as of 18:04, 24 February 2016 by Maintenance script (talk | contribs) (Initial automated import)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigationJump to search

VARIANCE.GIF

Command Summary

Finds the sample variance of a list.

Command Syntax

variance(list,[freqlist])

Menu Location

Press:

  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

TI-83/84/+/SE

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.

Formulas

The formula for variance used by this command is:

Template:TI-BASIC:Math

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

Template:TI-BASIC:Math

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

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

Related Commands