Population variance

Definition

Population variance is a measure of the dispersion of all values in a population from the population mean. It is calculated as the average of the squared differences between each value and the population mean.

5 Must Know Facts For Your Next Test

1. Population variance ($\sigma^2$) is different from sample variance ($s^2$).
2. The formula for population variance is $\sigma^2 = \frac{\sum (x_i - \mu)^2}{N}$, where $x_i$ are individual data points, $\mu$ is the population mean, and $N$ is the number of data points in the population.
3. Chi-square tests can be used to test hypotheses about population variance.
4. Population variance helps in understanding how spread out values are around the mean in a given dataset.
5. In statistical analysis, knowing whether you're dealing with a sample or a population determines if you use sample variance or population variance.

Review Questions

• What is the difference between population variance and sample variance?
• How do you calculate population variance?
• Why might you use a chi-square test to examine population variance?

Related terms

Sample Variance:

A measure of how spread out values are around the mean in a sample, calculated using $s^2 = \frac{\sum (x_i - \bar{x})^2}{n-1}$.

Chi-Square Distribution:

A distribution that describes how a test statistic is distributed if certain conditions are true. Often used for testing variances.

Standard Deviation:

$\sqrt{\text{Variance}}$, representing average distance from the mean. Population standard deviation uses $\sigma$, while sample standard deviation uses $s$.