Measures of spread

Use measures of spread to explain how data can differ despite sharing a central value.

Meaning

Spread describes how dispersed data are around a central value. The range is the maximum minus the minimum. Variance is based on squared deviations from the mean, and standard deviation is its square root.

Example

Treating 2, 4, and 6 as the entire population, the mean is 4 and the variance is The values 4, 4, and 4 have the same mean but variance 0.The deviations from 4 are −2, 0, and 2; simply adding them cancels to zero and hides the spread. Squaring removes signs and gives more weight to large deviations. Taking the square root returns standard deviation to the original units.Population variance and sample variance used for estimation may have different divisors. Standard deviation has the original units, while variance has squared units.

Practice for this concept

Scope and references

Topics

Range, deviations, variance, standard deviation

Learning goal

Use measures of spread to explain how data can differ despite sharing a central value.

Helpful background

Compare how far values lie from a central value.