The z-score converts any raw score into SDs from the mean—comparable across scales, tests and dimensions.
A z-score says how many standard deviations a value sits from its group mean: (x − μ)/σ. It makes a 42/60 exam and a 3.6/5 rating comparable, and it's the raw material for T-scores, percentiles and norm tables.
z = (x − μ) / σ
A participant scoring z = +1.4 on communication and −0.3 on planning shows a profile, not just a total—dimension radar charts run on z-scores.
Whenever you must compare apples to oranges—different scales, different cohorts, or a single person across dimensions.
z-scores inherit the distribution's shape; with skewed data or n < 20, the SD itself is unstable—percentiles are safer.
z keeps distance math (averaging, radar); percentile is friendlier to read. Report both, lead with percentile for clients.
Yes—below the mean. Range is unbounded, which is why T-scores (+50, 10 SD) exist for presentation.
Turn the concept into a live assessment：z-Score
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