Standard Deviation equation(s): (1) full population s.d. = SQRT ( SUM (Observed Value - Mean Value)2 ) / N (2) sample of full population s.d. = SQRT ( SUM (Observed Value - Mean Value)2 ) / ( N - 1 ) where N is the number of Observed values.
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Arithmatic Mean
b-a/6
Formula for standard error (SEM) is standard deviation divided by the square root of the sample size, or s/sqrt(n). SEM = 100/sqrt25 = 100/5 = 20.
Standard deviation (SD) is neither biased nor unbiased. Estimates for SD can be biased but that depends on the formula used to calculate the estimate.
The z score is calculated from the distance of a value from the distribution center divided by the standard dev. (x-xbar)/st. dev