Variance

Definition

Variance measures the spread of data points in a dataset relative to the mean. It is calculated as the average of the squared differences from the mean.

5 Must Know Facts For Your Next Test

1. Variance quantifies how much individual data points differ from the mean.
2. The formula for variance in a population is $$\sigma^2 = \frac{\sum (x_i - \mu)^2}{N}$$, where \(x_i\) represents each data point, \(\mu\) is the population mean, and \(N\) is the number of data points.
3. For a sample, variance is calculated using $$s^2 = \frac{\sum (x_i - \bar{x})^2}{n-1}$$, where \(x_i\) represents each data point, \(\bar{x}\) is the sample mean, and \(n\) is the sample size.
4. Variance can never be negative because it involves squaring each difference from the mean.
5. A higher variance indicates greater spread in the data points around the mean.

Review Questions

• What does variance measure in a dataset?
• How do you calculate variance for a population?
• Why can variance never be negative?

Related terms

Standard Deviation: The square root of variance; it provides a measure of spread in the same units as the original data.

Mean: The average of all data points in a dataset; calculated by summing all values and dividing by their count.

Range: The difference between the highest and lowest values in a dataset; gives an indication of overall spread.