Math
Standard Deviation Calculator
Calculate mean, variance, and standard deviation from values.
Inputs
Adjust the assumptions to match your scenario. Results update instantly.
Results
Primary outputs and comparison insights are built from the current inputs.
Mean
30
Average of the data points.
Variance
200
Average of squared deviations from the mean.
Standard deviation
14.14
Square root of the variance.
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How this calculator works
The Standard Deviation Calculator computes the mean, variance, and standard deviation for a set of data points. Enter value 1, value 2, and value 3 to estimate mean, variance, and standard deviation. The calculator updates instantly and adds a comparison table plus chart so you can test the sensitivity of the result before you use it in a decision.
Quick guide
Jump straight to the section you need, then return to the calculator.
Inputs
- First data point.
- Second data point.
- Third data point.
- Fourth data point.
- Fifth data point.
Outputs
- Average of the data points.
- Average of squared deviations from the mean.
- Square root of the variance.
Assumptions
- Population standard deviation (divides by n).
- All five values are used.
Tips
- Use sample std dev (n−1) for small samples from a larger population.
- Lower std dev means less spread around the mean.
Formula guide
Use these formulas to audit the output or explain it to someone else.
3 formulas
Usage examples
Review a ready-made scenario, copy it, then tweak inputs to match your case.
Example
Test scores spread
Inputs
- Example input Value 1: 72
- Example input Value 2: 85
- Example input Value 3: 90
- Example input Value 4: 68
- Example input Value 5: 95
Outputs
- Example result Mean: 82
- Example result Variance: 107.6
- Example result Standard deviation: 10.37
A std dev of ~10 on test scores means most scores fall within 10 points of the average.
Std Dev by Value 5
| Value 5 | Mean | Standard deviation |
|---|---|---|
| 30 | 26 | 10.2 |
| 40 | 28 | 11.66 |
| 50 | 30 | 14.14 |
| 60 | 32 | 17.2 |
| 70 | 34 | 20.59 |
Outliers increase standard deviation significantly.
Spread sensitivity
Focus point
30
10.2
Position
#1 of 5
Original order
Share of total
13.82%
Total: 73.8
Outliers increase standard deviation significantly.
References
- Statistical measures of dispersion
- Standard deviation fundamentals
FAQ
Common questions
What does the Standard Deviation Calculator do?
The Standard Deviation Calculator computes the mean, variance, and standard deviation for a set of data points. Enter value 1, value 2, and value 3 to estimate mean, variance, and standard deviation. The calculator updates instantly and adds a comparison table plus chart so you can test the sensitivity of the result before you use it in a decision. It is part of our math toolkit.
What inputs do I need?
Typical inputs include First data point., Second data point., Third data point..
How are the results calculated?
We follow the formulas and assumptions outlined in the "How this calculator works" section. You will see outputs like Average of the data points., Average of squared deviations from the mean., Square root of the variance..
Can I share or download the results?
Use the Copy link or Print buttons to share your results. If a table or chart appears, you can download the data as CSV.
Is my data stored?
No. Calculations run in your browser and we do not store your inputs.
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