Standard Deviation Calculator Using Mean
Calculate the standard deviation of a set of numbers using the mean. Enter numbers separated by commas or spaces, and get the population or sample standard deviation with step-by-step explanation.
Published by:
isCalculator Editorial Team
Was this calculator helpful?
How to use this tool?
This calculator computes the standard deviation of a dataset using the mean. It supports both population and sample standard deviation.
- Enter your data in the "Data Set" field. Separate numbers with commas or spaces (e.g.,
10, 12, 23, 23, 16). - Select the type:
- Population Standard Deviation – use when your data represents the entire group.
- Sample Standard Deviation – use when your data is a sample from a larger population. Requires at least 2 data points.
- Click "Calculate". The result shows the standard deviation rounded to 4 decimal places.
- Review the step-by-step breakdown below the result, which includes the mean, squared differences, variance, and final standard deviation.
Note: All numbers are treated as decimal values. Invalid entries (e.g., letters) will trigger an error message.
Previous Results
| Result | Inputs | Date |
|---|
Frequently Asked Questions
Standard deviation measures the dispersion of a dataset relative to its mean. A low standard deviation indicates data points are close to the mean, while a high standard deviation indicates data points are spread out.
Population standard deviation (σ) uses the entire dataset, dividing by n. Sample standard deviation (s) estimates the population from a sample, dividing by n-1 to correct bias.
Enter numbers separated by commas or spaces. For example: 10, 12, 23, 23, 16 or 10 12 23 23 16.
