| Property | Value |
|---|---|
| Hex Value | $BB0E |
| Categories | |
| Localizations |
|
variance(
Overview
Returns the variance of the elements in list with frequency freqlist.
Availability: Token available everywhere.
Syntax
variance(list[,freqlist])
Arguments
| Name | Type | Optional |
|---|---|---|
| list | list | |
| freqlist | list | Yes |
Location
2nd, list, MATH, 8:variance(
Description
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:
(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 \(\overline{x}\) is the mean with frequencies included.
Related Commands
Source: parts of this page were written by the following TI|BD contributors: burr, DarkerLine, GoVegan, kg583, thornahawk.
History
| Calculator | OS Version | Description |
|---|---|---|
| TI-83 | 0.01013 | Added |
Created: February 23, 2023 23:15:01