doomath Calculator
Statistics & Standard Deviation Calculator
Compute arithmetic mean, median, sample standard deviation (s), population standard deviation (σ), variance, sum of squares, and standard error of the mean.
InputsChange a value to recalculate instantly
ResultUpdates as you type
FORMULA & STEPSStatistics & Standard Deviation Calculator — Mathematical Derivation & Steps
3 StepsSequential Calculation Breakdown
1
Mean
Add the values and divide by the number of observations.
2
Squared deviations
Measure the total squared distance from the mean.
3
Standard deviations
Divide by n−1 for a sample or n for a population.
λ DooMathWork with this calculation
Local · deterministic · optionalQuick mathNatural-language-style shortcuts for deterministic arithmetic.
Calculator guide
How to use the Statistics & Standard Deviation Calculator
Compute arithmetic mean, median, sample standard deviation (s), population standard deviation (σ), variance, sum of squares, and standard error of the mean.
01Set inputsChoose values, units and assumptions.
02Apply the modelSample: s = √[∑(x_i - x̄)² / (n - 1)]; Population: σ = √[∑(x_i - μ)² / n]; SEM = s / √n
03Read the resultCheck the output against the assumptions before using it.
What this calculator does
Input numeric dataset values. The statistical engine computes deviations from the mean, squared differences, sample/population variance, and standard error.
Formula & method
Sample: s = √[∑(x_i - x̄)² / (n - 1)]; Population: σ = √[∑(x_i - μ)² / n]; SEM = s / √n
Assumptions & notes
- Sample standard deviation uses Bessel's correction (n - 1) to provide an unbiased estimator.
- Variance measures the average squared dispersion from the distribution center.
- Standard error (SEM) estimates precision of the sample mean.