Difference between revisions of "Variance"
(Created page with "The <b> variance </b> of a data set is a measure of how "spread out" the data points are in general. ==Formula== ===Population=== For a dataset <math>X = \{ x_1, x_2, x_3, \d...") |
|||
| Line 7: | Line 7: | ||
===Sample=== | ===Sample=== | ||
Because of <b>Bessel's correction</b> the variance if <math>X</math> is a [[sample]] is calculated according to the slightly different formula <cmath>V = \frac{1}{n-1}\sum_{i=1}^n (x_i - \overline{x})^2.</cmath> | Because of <b>Bessel's correction</b> the variance if <math>X</math> is a [[sample]] is calculated according to the slightly different formula <cmath>V = \frac{1}{n-1}\sum_{i=1}^n (x_i - \overline{x})^2.</cmath> | ||
| + | |||
{{stub}} | {{stub}} | ||
| + | [[Category:Statistics]] | ||
Latest revision as of 19:16, 3 March 2022
The variance of a data set is a measure of how "spread out" the data points are in general.
Formula
Population
For a dataset 
with mean 
the formula for variance if 
is a population is ![\[V = \frac{1}{n}\sum_{i=1}^n (x_i - \overline{x})^2.\]](http://latex.artofproblemsolving.com/b/4/c/b4c75e6bef818578a9483a944580f344bcf1cb09.png)
Additionally, 
where 
is the population standard deviation.
Sample
Because of Bessel's correction the variance if is a sample is calculated according to the slightly different formula ![\[V = \frac{1}{n-1}\sum_{i=1}^n (x_i - \overline{x})^2.\]](http://latex.artofproblemsolving.com/a/4/d/a4d2cd80aafdc103d50eb4f69dbf4ece5edd742a.png)
This article is a stub. Help us out by expanding it.
