The standard error describes the variability of sample means under repeated independent sampling.
Standard Deviation of Sample Mean Calculator
Form
Results
Standard deviation of the sample mean (σX̄)
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Table of Contents
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What is Standard Deviation?
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How to Use This Calculator
- Enter or select Population standard deviation (σ), Sample size (n).
- 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
SE = σ/√n
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Variables Explained
| Input | What it means |
|---|---|
| Population standard deviation (σ) | The spread of individual observations around their mean, in the data’s original units. |
| Sample size (n) | Number of observations or responses in the sample, rather than the population size. |
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Worked Example
Population standard deviation 12 with sample size 36 gives SE=2.
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Why Use This Calculator?
Estimate how much an average may vary across independent samples.
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Common Mistakes
- This is the spread of sample means, not the spread of individual observations.
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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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