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Z Scores

Z Scores

The z score of an observation xi, taken from a population with mean m and standard deviation s, is denoted by z and is calculated as follows:

z = (xi - m) / s

The z score is a measure of the number of standard deviations that an observation is above or below the mean. Since s is never negative, a positive z score indicates that the observation is above the mean, a negative z score that the observation is below the mean. Note that z is a dimensionless value, and is therefore a useful measure by which to compare data values from two different populations (and thus possibly measured by different units).



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