ClarityHow to use this tool
- Enter numbers, treat values as.
- Select Calculate to view the result.
- Check the method and assumptions below before using the result.
Input reference and sample values
Use the units and choices shown for each field. Sample values are provided for practice, not as recommendations.
| Input | Format and units | Sample |
|---|---|---|
| Numbers | Keep the structure and separators shown in the sample. Line breaks are retained in this input. | 2, 4, 4, 4, 5, 5, 7, 9 |
| Treat values as | Choose Entire population / Sample of a population. | Entire population |
Result for these sample inputs
2
- Variance
- 4
- Mean
- 5
- Count
- 8
Select Try the example in the form to load these values and calculate them again. This replaces the current form inputs. Compare the result with the method and worked explanation below.
The method, explained
Variance is the sum of squared distances from the mean divided by N for a population, or N − 1 for a sample. Standard deviation is the square root of variance. The calculation uses an incremental algorithm to reduce numerical error.
For 2, 4, 4, 4, 5, 5, 7 and 9, the mean is 5. Population variance is 4 and population standard deviation is 2. Sample deviation is approximately 2.13809.
What to keep in mind
Sample mode needs at least two observations. Separate values with commas, spaces or semicolons; use dots for decimals, not thousands separators. This is an unweighted calculation.
Common questions
Which mode should I choose?
Choose population if these are all values you want to describe. Choose sample when estimating population variability from a sample.
What units does the result use?
Standard deviation uses the original measurement unit. Variance uses that unit squared.
Methodology maintained by ClarityKit. How these tools are built and checked.