Z-Score Calculator
Calculate standard Z-scores and find corresponding percentage ranks or normal distribution probabilities step-by-step.
Interactive Z-Score Calculator Workspace
Normal Distribution Analysis
Step 1: Calculate Z-score using formula:
z = (x - μ) / σ = (135 - 100) / 15 = 2.3333
Step 2: Map standard normal cumulative density (percentile):
The score of 135 is exactly 2.3333 standard deviations above the population average of 100.
• Data scoring below 135: 99.0185%
• Data scoring above 135: 0.9815%
• Probability of scoring between -2.33 and +2.33: 98.0369%
Mathematical Formula & Variables
z = (x - μ) / σThe Z-score represents how many standard deviations a raw score x is above or below the population mean μ.
Variable Definitions
| Symbol | Description |
|---|---|
| z | Standardized Z-score |
| x | The raw value or score to standardize |
| μ | The population mean |
| σ | The population standard deviation |
How to Use the Z-Score Calculator
- Input the raw data score (x) you want to evaluate.
- Input the mean (μ) of your population.
- Input the standard deviation (σ) of your population.
- Read the Z-score and the corresponding normal distribution probability (p-value).
Practical Example Calculation
Scenario Context: Standardizing an SAT score of 1300 (x) where the population mean is 1000 (μ) and the standard deviation is 200 (σ).
Frequently Asked Questions
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