Math
Calculator for Standard Deviation
Mean, population standard deviation and sample standard deviation for one list of numbers.
Add to workspaceYour numbers
Result dey update as you type; no Calculate button dey. All calculation dey run inside your browser.
Result
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Enter at least one number; separate numbers with commas or spaces.
How the result break down
| Quantity wey we dey count | Value wey e get |
|---|---|
| Count (n) | — |
| Mean | — |
| Sum of squared deviations | — |
| Variance for whole population | — |
| SD for whole population | — |
| Variance for sample | — |
| SD for sample | — |
| Smallest / biggest | — |
Sample SD no get defined value for only one number (e dey divide by n − 1 = 0), so dem go show — for dat case.
Formula
Mean = Σx ÷ n. Population SD = √[Σ(x − mean)² ÷ n]; sample SD dey use n − 1 instead of n. Population variance na Σ(x − mean)² ÷ n and sample variance na Σ(x − mean)² ÷ (n − 1).
Example wey show the calculation
For 12, 15, 18, 20, 25: mean = 90 ÷ 5 = 18. Squared deviations na 36, 9, 0, 4 and 49; all of dem add up to 98. Population SD = √(98 ÷ 5) = √19.6 = 4.4272 (4.427189 if you show more places). Sample SD = √(98 ÷ 4) = √24.5 = 4.9497. Use Reset example above to get dis same result, then replace di list with your own data.
Where e fit work and limits
Every entry for the list must be finite number. Use population SD if the list na the whole group wey you want study; use sample SD if observations dey estimate a bigger population. Sample SD no get defined value for one number alone. Outliers fit affect standard deviation well well; e dey describe spread, no be distribution shape. We round display to 4 decimal places.
Questions wey people dey ask often
Population or sample SD — which one make I use?
Use population SD (÷ n) when your numbers na di whole group wey concern you. Use sample SD (÷ n − 1) when dem na sample and you dey estimate di spread of bigger population.
Why sample SD bigger?
E dey divide by n − 1 instead of n, to correct for di fact say dem fit di sample mean to di sample itself. Di gap dey reduce as n dey grow.
Wetin if I enter only one number?
Population SD na 0 (no spread), and sample SD no get defined value. Dem show am as — because n − 1 na zero.
The order of the numbers matter?
No. If you rearrange the list, mean and standard deviation no go change.
Entries wey no be numbers na error?
Yes. Invalid entries or numbers wey no finite dey pause calculation and show error; we no silently skip dem. Correct the list before you read result.
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Results na estimates; dem no replace advice from qualified professional.