Standard scores (z-scores) — Data, 14–17 years
A way to say how far a value is from its group’s mean, measured in standard deviations. Data, 14–17 years.
Idea
A z-score changes a raw value into a position relative to its group. A z-score of 0 is exactly average; +2 means two standard deviations above average, and −1 means one below. It lets unlike scales speak a common language.
Why use it?
Raw scores can mislead when tests or groups use different scales or levels of difficulty. Standardising removes the units and keeps the relative position, so a result can be compared fairly with another result from a different distribution.
Worked example
A test score is 78, the group mean is 70, and the standard deviation is 4. First find the difference: 78 − 70 = 8. Then divide by 4: z = 8/4 = 2. The score is therefore two standard deviations above the group mean.
Common trap
A positive z-score does not automatically mean a good result, and a negative one does not mean a bad result. The sign only says which side of the mean the value lies on; what counts as good depends on what the measurement represents.
Where it appears
Universities and employers may compare results from tests with different averages and spreads by using standard scores. In science, z-scores can flag an observation that is unusually far from a model’s centre, while still requiring a sensible check of the data.
Keep exploring
Other languages
Loading MyLeoNes™…