DEFINITION of 'Variance'

A measurement of the spread between numbers in a data set. The variance measures how far each number in the set is from the mean. Variance is calculated by taking the differences between each number in the set and the mean, squaring the differences (to make them positive) and dividing the sum of the squares by the number of values in the set.


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Variance is used in statistics for probability distribution. Since variance measures the variability (volatility) from an average or mean, and volatility is a measure of risk, the variance statistic can help determine the risk an investor might take on when purchasing a specific security.

A variance value of zero indicates that all values within a set of numbers are identical; all variances that are non-zero will be positive numbers. A large variance indicates that numbers in the set are far from the mean and each other, while a small variance indicates the opposite.

Statisticians use variance to see how individual numbers relate to each other within a data set, rather than using broader mathematical techniques such as arranging numbers into quartiles. A drawback to variance is that it gives added weight to numbers far from the mean (outliers), since squaring these numbers can skew interpretations of the data.

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