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Z-Score Calculator

Calculate the z-score using one of three methods: a single value with known parameters, a sample mean, or comparing two sample means.

Z-score formulas

Populationz = x − μσ
Samplez = x − x̄s
Two-samplez = x̄1 − x̄2√σ12/n1 + σ22/n2

Worked examples

  1. A score of 1350 on a test with mean 1050 and SD 200.

    1. z = 1350 − 1050200 = 1.5

    Answer: z = 1.5 → about the 93.3rd percentile

  2. Class A: mean 78, σ 10, n 50. Class B: mean 74, σ 12, n 60.

    1. SE = √100/50 + 144/60 = √4.4 ≈ 2.098
    2. z = (78 − 74) ÷ 2.098

    Answer: z ≈ 1.91 (just under the 1.96 cut-off for 5% significance)

Tips & common mistakes

  • |z| > 2 is unusual (outside ~95% of a normal distribution); |z| > 3 is rare.