# TI-BASIC:Variance

**Command Summary**

Finds the sample variance of a list.

**Command Syntax**

variance(*list*,[*freqlist*])

**Menu Location**

Press:

- 2ND LIST to enter the LIST menu.
- LEFT to enter the MATH submenu.
- 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

# 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:

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

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

With frequencies *w,,i,,*, the formula becomes

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