# What is the difference between standard deviation and variance? Thanks

embizze | High School Teacher | (Level 1) Educator Emeritus

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A variable (such as height,etc...) is measured. There is an expected value for the variable -- the parameter associated with the population.

The absolute deviation is the distance each such measurement is from the expected value. The deviation is the sum of the differences away from the expected value, and thus will be zero. So we compute the square of the deviations which is the variance.

The variance is a measure for how spread out the data are.

Unfortunately, when we square the data value we also square the units. So the variance for a sample of heights measured in inches is in inches squared. That is not very helpful, so we take the square root of the variance. (Note that the sum of the deviations would be zero, but the sum of the deviations squared will not be, so we are taking the square root of a positive number)

The square root of the variance is the standard deviation.

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