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.
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Variance quantifies how much individual data points differ from the mean.
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.
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.
Variance can never be negative because it involves squaring each difference from the mean.
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.