Z-score

The Z-score (also called standard score) can be defined as the number of standard deviations away from the population mean that a certain datapoint is.

This can tells us how usual or unusual a datapoint is.

Example Let’s say we have this dataset

2,2,3,2,5,1,6

With mean and std $\mu =3,\sigma =1.69$.

Remember the definition of te z-score, then we can compute it for a datapoint $x$ by using the formula

$$z_x=\frac{x-\mu }{\sigma }$$

The numerator tells us how far the datapoint is from the mean. Dividing it by the standard deviation transforms the unit of measure from a “unit” to the number of standard deviations (we want to know how many standard deviations away we are from the mean).

Related

• Z-score is used in the z-test;
• Converting the values from raw values to z-scores is called standardization, which is a type of Normalization.

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#math/statistics resources:

• Z-score introduction | Modeling data distributions | AP Statistics | Khan Academy - YouTube