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Variance
Explanations > Social Research > Statistical principles > Variance Description | Example | Discussion | See also
DescriptionVariance is a measure of the spread in a list of numbers. It is commonly represented as s^{2} or s^{2} (sigma-squared). It is calculated as follows for a sample: VAR(X) = SS/(N-1) = (SUM(X_{i} - AVERAGE(X))) / (N-1) where N is the number of items in the list. If the list represents a complete population, then the division is by N (not N-1). VAR(X) = SS/N = (SUM(X_{i} - AVERAGE(X))) / N ExampleA set of measures, as in Column A below, can easily have its variance calculated.
DiscussionVariance is an improvement on Sum of the Squares, SS, as a measure of spread, as it makes the measure independent of the length of the list of numbers. Dividing SS by (N-1) is due to the 'degrees of freedom' issue. Variance is a part of many other calculations, from standard deviation to ANOVA. Variance has the disadvantage that it is measured in squared units as compared with the number in the original list. This is why it is represented as s^{2,} as sigma represents the standard deviation. In Microsoft Excel, the formula VAR() may be used to automatically calculate the variance of a range of measures. See also |
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