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Calculating z-scores

Calculating z-scores

Author: Ryan Ottman

In this tutorial, you will learn what a z-score is.

Furthermore, with a given mean and standard deviation, you will be able to calculate the z-score of any data value, and you will also be able to find the data value that will have the given z-score

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What is a z-score?

Given any data set, the z-score for any given data point within the data set is the number of standard deviations that data point is above the mean.

How do we calculate a z-score?

If we have the mean left parenthesis mu right parenthesis and standard deviation left parenthesis sigma right parenthesis of a data set, we can calculate the z-score left parenthesis z right parenthesis of any given data point left parenthesis x right parenthesis with the following formula

z equals fraction numerator x minus mu over denominator sigma end fraction

Calculating x from a z-score

We might also want to go in the opposite direction, we might want to know what data value would produce a given z-score. To do this, we merely have to solve the above equation for x 

x equals mu plus z sigma

and plug in mu comma space z and sigma