## Standardized Variables

standardized variable

Variable with a mean of 0 and a standard deviation equal to 1

Distribution of costs or revenues can be transformed or standardized. A standardized variable has a mean of 0 and a standard deviation equal to 1. Any distribution of revenue, cost, or profit data can be standardized with the following formula:

x - p where z is the standardized variable, x is the outcome of interest, and p and a are the mean and standard deviation of the distribution, respectively. If the point of interest is 1a away from the mean, then x - p = a, so z = a/a = 1.0. When z = 1.0, the point of interest is 1a away from the mean; when z = 2, the value is 2a away from the mean; and so on. Although the standard normal distribution theoretically runs from minus infinity to plus infinity, the probability of occurrences beyond 3 standard deviations is very near zero.

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