Mean, SD & SEM Calculator
Mean, standard deviation, standard error, median, quartiles and CI from raw data.
Enter your values to see the result.
SD is the sample standard deviation (n − 1). SEM = SD ÷ √n, and the confidence interval of the mean uses the t distribution with n − 1 degrees of freedom.
Processing and privacy
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Read the privacy policyHow this calculation works
Understand the method, inputs and limits behind your result.
- Formula
- Mean = Σx/n; sample SD = √[Σ(x − mean)²/(n − 1)]; SEM = SD/√n. Confidence intervals use a t critical value with n − 1 degrees of freedom.
- Variables
- Values (paste a column, or separate with commas or spaces)
- Confidence level: 90%, 95%, 99%
- Units
- Use the units shown beside each input. Counts and ratios are dimensionless unless labeled otherwise.
- Example
- Ten readings averaging 13.53 with SD 1.10 have an SEM of 0.35 and a 95% confidence interval of 12.74 to 14.32.
- Assumptions
- SD is the sample standard deviation (n − 1). SEM = SD ÷ √n, and the confidence interval of the mean uses the t distribution with n − 1 degrees of freedom.
- Source
- ToolzHive calculation guide and calculator implementation. External reference verification is pending.
- Last reviewed
- Review date not yet recorded.
Methodology & References
The method depends on the selected model and input options. Review the assumptions and references above before interpreting the result.
- Paste your values from a spreadsheet column, or type them separated by commas or spaces.
- Choose the confidence level for the interval of the mean.
- Copy the statistics, or the ready-made reporting sentence.
Interpretation and limitations
- What is the difference between SD and SEM? SD describes how spread out the data are. SEM describes how precisely the mean is estimated, and it shrinks as the sample grows.
- Which should I report? Report SD to describe your sample and a confidence interval to show the precision of the mean. Avoid using SEM just because it looks smaller.
References
External reference verification is pending. The formula and examples describe the current ToolzHive implementation.
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Clear instructions
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How to use the Mean, SD & SEM Calculator
Mean, standard deviation, standard error, median, quartiles and CI from raw data.
- 1 Paste your values from a spreadsheet column, or type them separated by commas or spaces.
- 2 Choose the confidence level for the interval of the mean.
- 3 Copy the statistics, or the ready-made reporting sentence.
Example and practical tips
Ten readings averaging 13.53 with SD 1.10 have an SEM of 0.35 and a 95% confidence interval of 12.74 to 14.32.
Frequently asked questions
What is the difference between SD and SEM?
SD describes how spread out the data are. SEM describes how precisely the mean is estimated, and it shrinks as the sample grows.
Which should I report?
Report SD to describe your sample and a confidence interval to show the precision of the mean. Avoid using SEM just because it looks smaller.
Practical guides
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How to Use Mean, SD & SEM Calculator
Paste your data to get the mean, standard deviation, standard error of the mean, 95% CI, median, quartiles, variance and range in one step.
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