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