Understanding Z Scores

Z scores standardize values using population parameters, indicating how many standard deviations a value is from the mean. This is crucial for comparing values from different normal distributions and calculating probabilities.

Calculation Example

For a population with μ=100 and σ=15, a raw score of 125 converts to:

z = (125 - 100) / 15 = 1.6667

Common Reference Values

Z Score	Percentile	Probability Below
-3.0	0.1%	0.0013
-2.0	2.3%	0.0228
-1.0	15.9%	0.1587
0.0	50.0%	0.5000
1.0	84.1%	0.8413
2.0	97.7%	0.9772
3.0	99.9%	0.9987

Frequently Asked Questions

Can z scores be negative?

Yes, z scores can be negative when the raw score is below the population mean.

What does a z score of 0 mean?

A z score of 0 indicates the raw score is exactly equal to the population mean.

When should I use population vs sample parameters?

Use population parameters (μ, σ) when you have data for the entire population. For samples, use sample mean (x̄) and sample standard deviation (s).

Z Score Calculator

Result

Normal Distribution Visualization

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Z Score Calculator - Standardize Any Value

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