Calculate the Z-score (standard score) for any data point. Find where a value sits relative to the mean and what percentile it corresponds to.
Measures how many standard deviations a value is from the mean. Z = (x-μ)/σ. Z=0 equals the mean.
Z above +2 or below -2 is unusual (5% of normal distribution). Most values fall between -2 and +2.
Z=0 = 50th percentile, Z=1 ≈ 84th, Z=2 ≈ 97.7th, Z=-1 ≈ 16th percentile.
Z above +1 = better than 84% of test-takers. Above +2 = better than 97.7%.
Both measure distance from mean in SD units. T = 10Z+50, giving mean 50 and SD 10. T-scores are used in educational assessments.