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Thorne and Giesen Book Cover
Statistics for the Behavioral Sciences, 4/e
Michael Thorne, Mississippi State University -- Mississippi State
Martin Giesen, Mississippi State University -- Mississippi State
Measures of Dispersion and Standard Scores

Symbols and Formulas

SYMBOLS

SymbolStands For
ADaverage deviation
Rrange
s2population variance
s2sample variance
spopulation standard deviation
ssample standard deviation
sapproxan approximation of s; sapprox = R/4
Ssum of squares or the numerator of variance
zstandard score or z score

FORMULAS

Formula 6-1. Formula for calculating the range

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Formula 6-3. Formula for computing AD from a frequency distribution

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To find AD, the first step is to subtract the mean from each score. Next, multiply the absolute values of the differences by their frequencies and sum the results. Finally, divide the numerator by N to find the average deviation.

Formula 6-8. Computational formula for s2, the sample variance

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Formula 6-9. Computational formula for s2, the sample variance, for a frequency distribution

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The numerator is the computational form of the sum of squares. To get it, sum the squared scores and subtract from this value the sum of the scores squared divided by sample size. Then divide the whole thing by N - 1.

Formula 6-14. Computational formula for sample standard deviation

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Formula 6-15. Computational formula for sample standard deviation for a frequency distribution

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s is simply the square root of the formula for sample variance.

Formula 6-17. Formula for finding a z score from a raw score using sample statistics

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Formula 6-19. Formula for finding a raw score from a z score using sample statistics

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Formula 6-19 is obtained by solving Formula 6-17 for X.









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