A z-score locates a value in standard-deviation units relative to a mean.
Z-score Calculator
Form
Results
Z-score (z)
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Table of Contents
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What is Z-Score?
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How to Use This Calculator
- Enter or select Experimental result (X), Mean value (μ), Standard deviation (σ).
- Check the unit beside each measurement. For a percentage or rate, use the scale and time period stated in the form.
- Choose Calculate, then compare the output with the formula and example below. If you change a value or option, calculate again to update the result.
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Formula Used
z = (x−μ)/σ
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Variables Explained
| Input | What it means |
|---|---|
| Experimental result (X) | Use the measured or stated value for this item, with the unit or category shown beside the field. |
| Mean value (μ) | The numeric input for the relationship being evaluated. |
| Standard deviation (σ) | The spread of individual observations around their mean, in the data’s original units. |
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Worked Example
With x=85, μ=70 and σ=10, z=1.5.
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Why Use This Calculator?
Compare observations measured on different scales after standardization.
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Common Mistakes
- Standard deviation must be positive. A z-score alone does not prove the data are normally distributed.
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Frequently Asked Questions
Does a calculated statistic prove a conclusion?
A statistic describes the supplied data under stated assumptions. Sampling design, missing observations and the suitability of the model still determine what can reasonably be concluded.
Should I include every observation?
Use the observations required by your study design and state any exclusion rule. Removing values only because they change the answer can bias the analysis.
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Sources & References
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