Recover an original observation from its z-score, mean and standard deviation.
Raw Score Calculator
Form
Results
Raw score (X)
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Table of Contents
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What is Raw Score?
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How to Use This Calculator
- Enter or select Mean value (μ), Standard deviation (σ), Z-score (z).
- 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
x = μ + zσ
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Variables Explained
| Input | What it means |
|---|---|
| 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. |
| Z-score (z) | Use the measured or stated value for this item, with the unit or category shown beside the field. |
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Worked Example
A z-score of 1.5 with mean 70 and standard deviation 10 gives 85.
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Why Use This Calculator?
Translate a standardized position back into the original measurement units.
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Common Mistakes
- Use the same mean and standard deviation that were used to standardize the value.
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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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