Variance

Definition

Variance is a measure of how much the values in a data set differ from the mean. It quantifies the spread or dispersion of the data.

5 Must Know Facts For Your Next Test

1. The formula for variance in a population is $$\sigma^2 = \frac{\sum (x_i - \mu)^2}{N}$$ and for a sample is $$s^2 = \frac{\sum (x_i - \bar{x})^2}{n-1}$$.
2. A high variance indicates that data points are spread out over a large range of values.
3. A low variance indicates that data points are close to the mean.
4. Variance is always non-negative because it is the average of squared deviations.
5. Variance units are the square of the units of the original data.

Review Questions

• What does a high variance signify about a dataset?
• How does one calculate variance for a sample versus a population?
• Why can variance never be negative?

Related terms

Standard Deviation:

The square root of the variance, providing a measure of spread in the same units as the data.

Mean:

The average value of all observations in a dataset.

Range:

The difference between the maximum and minimum values in a dataset, indicating its total spread.