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# Z-score

## Description

Thus z is a measure of how far away a measurement is from the mean, measured in standard deviations.

Calculation:

z = (X - X-bar)/S

Where X is a measured value, X-bar is the mean of all measured values and S is the standard deviation of all measured values.

## Example

John gets a mark of 64 in a physics
test, where the mean is 50 and the standard deviation is 8.

Jane gets a mark of 74 in a chemistry test, where the mean is 58 and the
standard deviation is 10.

John's z = (64 - 50) / 8 = 1.75

Jane's z = (74 - 58) / 10 = 1.6

Although Jane's score is higher, John's score is further above the mean, and it might be concluded that John has achieved greater success.

## Discussion

The z-score provides a simple measure by which different measures can be compared in terms of their deviation from the mean. This is often called standardization.

The z-score in use generally assumes parametric data.

Z-test

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