# z-score

A z-score says how many standard deviations a value is from the mean: (value minus mean) divided by standard deviation. Positive means above the mean, negative means below.

Statistics (university) · Part 01: Describing data · Card 9 of 9 · Last updated 2026-10-19

## Analogy

It is a ruler measured in standard-deviation steps, so you can compare scores from different tests.

## Example

**Standardising a score**

Exam mean 70, SD 4
Score 78: z = (78 - 70) / 4 = 2
Score 62: z = (62 - 70) / 4 = -2
Score 70: z = 0

## In practice

Comparing a maths score with a French score is fair only after both are turned into z-scores.

## Practice

### Flashcards

- **What is the z-score formula?** (value minus mean) divided by standard deviation.

## Questions people ask

### What does a z-score of 2 mean?

The value sits 2 standard deviations above the mean. In roughly bell-shaped data, about 95 percent of values lie within 2 standard deviations of the mean, so a z-score of 2 is fairly unusual. Only about 2.5 percent of values sit that far above.

### How do z-scores let you compare different tests?

Raw marks depend on each test's average and spread. A z-score removes both, leaving a unit-free position. A student with z = 1.5 in maths and z = 0.5 in French did relatively better in maths, even if the raw marks look similar.

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