Population variance

Definition

Population variance is a measure of how data points differ from the mean of a population. It is calculated as the average of the squared differences from the mean.

5 Must Know Facts For Your Next Test

1. Population variance quantifies the spread of data points in a population.
2. The formula for population variance is $\sigma^2 = \frac{\sum (X - \mu)^2}{N}$, where $X$ represents each value, $\mu$ is the mean, and $N$ is the number of values.
3. In hypothesis testing, especially when using chi-square distribution, population variance helps test whether observed variances match expected variances.
4. A large population variance indicates that data points are widely spread out around the mean.
5. Population variance differs from sample variance; sample variance uses $n-1$ in its calculation to correct bias.

Review Questions

• What does population variance measure?
• How do you calculate population variance?
• Why is population variance important in hypothesis testing using chi-square distribution?

Related terms

Chi-Square Distribution:

A statistical distribution used to test hypotheses about categorical variables and variances.

Sample Variance: An estimate of population variance based on sample data, calculated as $s^2 = \frac{\sum (X - \bar{X})^2}{n-1}$.

Hypothesis Testing:

\text{A method used to determine if there is enough statistical evidence to support a certain belief or hypothesis about a parameter.}