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Z-Score Calculator — Standard Score & Percentiles
Compute normal distribution Z-scores, standard deviations from mean, and percentiles.
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Normal Distribution Scores
Standard Normal Z-Score Formula
Transparent mathematical methodology explained in plain English.
Z = (X - μ) / σ Normalizes a score X relative to population mean μ and standard deviation σ.
Variables Explained:
- X: Individual raw data point.
- μ: Mean of the distribution.
- σ: Standard deviation (must be > 0).
Real Project Example
Exam Score of 85 with Mean 75 and Std Dev 5
Finding relative standing on normal curve.
Sample Project Inputs:
Raw Score X: 85
Mean μ: 75
Std Dev σ: 5
Step-by-Step Calculation:
- Deviation from mean: 85 - 75 = 10.
- Z = 10 / 5 = 2.0.
- A Z-score of +2.0 corresponds to the 97.72 percentile.
Calculated Answer: Z-Score = +2.0 (97.7th percentile).
Knowledge Base
Frequently Asked Questions: Z-Score Calculator
Click any question below to expand quick answers, formulas, and expert tips.
What does a Z-score of 0 mean?
A Z-score of 0 indicates that the data point is exactly equal to the mean of the distribution.