how to calculate a z score

A z score is a standardised score. That means, that it is the score in standard deviations away from the mean.

For example, Jo has an IQ of 115.

What is Jo's z score? Well, IQ has a mean of 100, and a standard deviation of 15. Jo is exactly one standard deviation higher than the mean, so the z score for her IQ is 1.

Jo has a friend Jay. Jay's IQ is 130. Since 130 is exactly two standard deviations above the mean (2 times 15), the z score for Jay's IQ is two.

z scores are useful because they give us the context of a number. They tell us if it is high or low, and how much.

This is how a z score is calculated:

First, you need the score itself (call it "x"), you need the mean, and you need the standard deviation (call it "sd").

z = (score - mean) /sd

In words: the score minus the mean, then divide by standard deviation. For Jo, this is 115-100)/15 which equals 1. For Jay, it is (130-100)/15 which equals 2.