How it works
Calculate population or sample standard deviation, variance, mean, sum, standard error, and margin of error. Inputs are calculated locally in the browser, and valid values are retained in the page URL for bookmarking.
Input query strings and outputs
Use an input name in this page’s URL as ?name=value, and join additional inputs with &. Portable shared links may instead use the compact ?ac= state parameter.
Input query strings
3-
?values=NumbersText · Required · Default: 10, 12, 23, 23, 16, 23, 21, 16
-
?sample=Treat the values as a sampleTrue or false · Optional · Default: false
-
?confidenceLevel=Confidence level for margin of errorChoice · Required · Default: 95 · Accepted values: 80, 90, 95, 98, 99
Outputs
7-
standardDeviationStandard deviationNumber · Primary output
-
varianceVarianceNumber
-
meanMeanNumber
-
sumSumNumber
-
countCountWhole number
-
standardErrorStandard errorNumber
-
marginOfErrorMargin of errorNumber
Formula notes
Population: σ = √[Σ(x − μ)²/n]; sample: s = √[Σ(x − x̄)²/(n − 1)]; margin = z·s/√n.
Input guidance
Use consistent units for every length or measurement in the same calculation. Results are educational mathematical estimates and should be checked before high-stakes use.