Mathematics · Statistics
Standard Deviation Calculator
Calculate population and sample standard deviation for six values.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Mean = 4.666666666666667.
- Sum of squared deviations = 27.333333333333332.
- Population σ = √(27.333333333333332 ÷ 6) = 2.1343747458109497; sample s = √(27.333333333333332 ÷ 5) = 2.3380903889000244.
Definition and formula
Standard deviation measures typical distance from the mean. Sample deviation uses N − 1 to estimate population spread from a sample.
Population σ = √[Σ(x − μ)² ÷ N]
Worked example
For 2, 4, 4, 4, 5, 9, the population standard deviation is about 2.13.
Common mistake
Choose population or sample deviation according to what the entered data represents.
How to learn with this calculator
Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.
Clear answers
Frequently asked questions
What does the Standard deviation do?
Calculate population and sample standard deviation for six values.
How does the Standard deviation work?
The calculator applies Population σ = √[Σ(x − μ)² ÷ N]. Standard deviation measures typical distance from the mean. Sample deviation uses N − 1 to estimate population spread from a sample.
What can I learn from the Standard deviation?
It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.
Does MW SysArc receive or store what I enter?
No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.
How should I use the result?
Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.
Last reviewed 2026-07-14. Calculations tested 2026-07-14.