Frequently Asked Questions
What does z = 0 mean?
z = 0 means the value equals the mean exactly. It corresponds to the 50th percentile: half of the data is below, half above (in a normal distribution).
Can I use z-scores to compare two different tests?
Yes. That is one of the main uses. If a student scores 80 on Test A (μ = 70, σ = 10, z = 1.0) and 85 on Test B (μ = 80, σ = 15, z = 0.33), their Test A performance is stronger relative to the population, even though the raw score is lower.
Do z-scores assume normality?
The z-score formula itself (X−μ)÷σ does not assume normality. But interpreting the result as a percentile using Φ(z) does assume the data follows a normal distribution. For non-normal data, use percentile rank directly on the data rather than the normal CDF.
What is the relationship between z-scores and standard normal tables?
Standard normal tables list Φ(z) = P(Z ≤ z) for the standard normal distribution. This calculator computes the same quantity numerically. z = 1.96 corresponds to Φ(1.96) ≈ 0.975, meaning 97.5% of the distribution falls below z = 1.96.
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Estimates for informational purposes only.
Important Disclaimer: Estimates for informational purposes only.
This calculator provides estimates for informational purposes only. Results are based on assumptions and may not reflect actual outcomes. Consult qualified professionals in relevant fields before making important decisions based on these results.