Standard Deviation Calculator — Population & Sample

Calculate mean, variance, and standard deviation for any dataset. Supports both population and sample formulas with step-by-step working.

Data set — comma or newline separated
Statistical Results — n = 8
Count (n)8
Sum (Σx)40
Min2
Max9
Range7
Q14
Q35.5
IQR1.5
Mean (μ)5
Median4.5
Mode4
Pop. Variance (σ²)4
Pop. Std Dev (σ)2
Sample Variance (s²)4.571428571
Sample Std Dev (s)2.138089935
Skewness0.65625
Excess Kurtosis-0.21875
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How to use this calculator

  1. 1

    Enter the mathematical parameters

    Enter the numerical values, expressions, or mathematical parameters into the Standard Deviation Calculator — Population & Sample.

  2. 2

    Select calculation method

    Select the calculation type, formula variant, or mathematical method if applicable.

  3. 3

    Solve the expression

    Press Calculate to solve the mathematical expression or equation.

  4. 4

    Verify the result

    Review the result and verify using step-by-step working or an alternative method where available.

Formula

Result = f(inputs, operation)

inputs
Numerical values, expressions, or parameters entered into the Standard Deviation.
operation
Mathematical operation, formula variant, or method applied to the inputs.
Result
Computed numerical or symbolic output.

Verify results using an alternative method or step-by-step working where available.

Glossary and Definitions

Operand
A value or expression on which a mathematical operation is performed.
Operator
A symbol (such as +, ×, ∫) that specifies the operation applied to operands.
Significant digits
The digits of a result that are meaningful given the precision of the inputs.
Closed form
An expression that can be evaluated in a finite number of standard operations.
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Frequently Asked Questions