Z-scores


Using z‑scores allows us to convert deviations from the mean into units of standard deviation, i.e. the number of standard deviations from the mean.

Note that doing this results in not having to worry about metres, pounds etc.

The unit of measurement is always standard deviations.

Calculating the z‑score

The z-score is very easy to calculate:  It is the raw score minus mean score, divided by the standard deviation

Why is this useful?

Z-scores make it possible to compare scores.  For example if a student got 85% in the final exam in history and 77% in the final exam in psychology, did that student do better in history?  Not necessarily.  If the class average for the history exam was 84% and the class average for the psychology exam was 70%, then clearly the student did better on the psychology exam.  But how much better?  To find this out it is necessary to calculate the z-score.

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