When to use this calculator
Find population standard deviation from a list of numeric observations. Uses population denominator N. Treats the entered observations as the whole population being described.
Explore the descriptive statistics calculators for other questions in this topic. For a related calculation, use the Population Variance Calculator: Find population variance for a variable-length numeric dataset.
PUTTING IT INTO PRACTICE
Population Standard Deviation: a worked example
The values below are an illustrative example, not a recommendation. Replace them with measurements or assumptions that match your question.
| Input | Example value |
|---|---|
| Data values separated by commas or spaces | 2,4,6,8 |
| Result | 2.236068 |
- Check the input labels and enter the example values above.
- Apply the relationship: Population SD = √(sum of squared deviations from mean/N)..
- The result is 2.236068 , rounded for display.
How to interpret your result
Uses population denominator N. Treats the entered observations as the whole population being described.
The mean, median, range and standard-deviation tools accept variable-length lists with their limits stated. Choose a sample or population denominator appropriately. A summary statistic does not validate the sampling process or explain causation.
Frequently asked questions
Should I use sample or population standard deviation?
Use population deviation for the complete population being described. Use the sample form when estimating variability from a sample under suitable assumptions.
When is the population standard deviation calculator useful?
Find population standard deviation from a list of numeric observations. Uses population denominator N. Treats the entered observations as the whole population being described.
How do I use the population standard deviation calculator?
Enter data values separated by commas or spaces. The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
Population SD = √(sum of squared deviations from mean/N)..
What should I check before using the result?
Uses population denominator N. Treats the entered observations as the whole population being described.
How are results rounded?
Scalar numbers display up to six decimal places, with scientific notation for very large or small values. Text, fraction, date and schedule outputs use the format described on the tool. Intermediate calculations use JavaScript floating-point arithmetic. Keep sensible precision for your measurements.
Further reading
For background on this topic, see NIST: exploratory data analysis ↗. This is a topic reference, not an external review or endorsement of this tool.
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