Microsoft KB Archive/41252

Formulas for Standard Deviation in Works

PSS ID Number: Q41252 Article last modified on 10-16-1998

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MS-DOS

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= SUMMARY =

The Works formula for calculating a standard deviation generates the precise standard deviation of the range listed. Some calculators and other programs generate a larger number because they use a formula for statistical estimation.

= MORE INFORMATION =

The Works standard deviation formula takes the square root of the result of the division of the sum of the squared deviations from the mean and the number of elements.

If you apply the formula to a random sample to estimate the standard deviation of a population, this formula could be multiplied by a factor to account for degrees of freedom. This factor is calculated by taking the square root of the result of the division of the number of elements and the number of elements minus the degrees of freedom. The following examples show these formulas symbolically:

STD = SQRT((DEVIATIONS)^2/ELEMENTS)

ESTD = SQRT((DEVIATIONS)^2/(ELEMENTS-DF))

FACTOR = SQRT(ELEMENTS/(ELEMENTS-DF))

The terms and definitions of these formulas are:

Term Definition —- ———-

STD The standard deviation

ESTD The estimated-population standard deviation calculated using sample data

FACTOR The number that can be used to multiply by STD to produce ESTD

DEVIATIONS The sum of squared deviations from the mean

ELEMENTS The number of cells (or numbers) in the range

DF Degrees of freedom, which in this context are always 1

KBCategory: kbother KBSubcategory: dworkskb:

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Version : 1.00 1.05 2.00 3.00 Platform : MS-DOS ============================================================================= Copyright Microsoft Corporation 1998.