Variance Calculator

Formula

First di mean x̄ = (sum of values) ÷ n. Then di sum of squared deviations SS = Σ(x − x̄)². Population variance, when di data na di whole group, na SS ÷ n. Sample variance, when di data na sample from bigger group, na SS ÷ (n − 1). Standard deviation na square root of variance, so e return to di original units. Di n − 1 divisor, wey dem call Bessel correction, dey compensate for di fact say sample own mean dey closer to im points than di true mean.

Example wey show the calculation

2, 4, 4, 4, 5, 5, 7, 9: di sum na 40 and n = 8, so di mean na 5. Di squared deviations na 9, 1, 1, 1, 0, 0, 4, 16, wey add up to SS = 32. Population variance = 32 ÷ 8 = 4.00 (SD 2.00); sample variance = 32 ÷ 7 = 4.57 (SD 2.14). Di sample figure big pass because e dey divide by di smaller number. Na di standard adjustment when you dey use sample estimate population.

Where e fit work and limits

Dis page only dey describe spread; e no dey tell you di distribution shape, identify outliers or decide whether mean na good summary. Variance dey use squared units, like square dollars or square centimetres. Na why people normally dey report standard deviation: e return to di original units. One extreme value fit raise variance plenty, so for skewed data, check median and interquartile range too. Sample variance need at least two values; with only one value, e no get defined result.

Version of di formula: b8bd891ff515 · Example don get check: 2026-10-31

Questions wey people dey ask often

Which variance I go use, population or sample?

Use population version when your data na everybody wey concern you, like all employees or all products wey you test. Use sample version when your data na part wey suppose represent bigger group, like survey or trial batch. Most real-world analysis dey use sample version.

Why dem dey divide by n − 1 for sample?

Because dem fit di sample mean to di same data, di squared deviations around am dey systematically small by small amount. If you divide by n − 1 instead of n, e dey correct dat bias on average. Na Bessel correction be dat.

Why dem dey square di deviations at all?

Plain deviations dey add up to zero by di definition of mean: positive and negative deviations dey cancel. Squaring dey make deviations no negative before you average dem, and e dey give larger deviations more weight.

Wetin be di difference between variance and standard deviation?

Standard deviation na square root of variance. Variance dey convenient for mathematics; standard deviation dey easier to interpret because e return to di original units, like dollars, centimetres or points.

Variance fit be zero?

Yes, when every value na di same, no spread dey at all. E no fit ever be negative because na average of squares.

Variance dey tell me about outliers?

Variance dey summarize di overall squared spread, and extreme values fit affect am plenty. E no fit identify outliers by itself. Check di sorted observations, range and interquartile range too.

Other tools wey relate to dis

• Calculator for Mean, Median and Mode — di centre of one data set
• Calculator for Standard Deviation — spread as one main figure
• Calculator for percentages — percentage changes and proportions