Variance and Standard Deviation
Also known as sigma · spread of data
Worked example: sd 12 → variance 144 — press Try an example to run it live, then adjust anything.
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Measuring the spread →
Grade 12Grade 12 Math
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Variance and Standard Deviation explained
Variance and standard deviation are the same fact in two costumes. Variance averages the squared deviations from the mean, which makes it mathematically well behaved — variances of independent quantities simply add — but leaves it in squared units, so the variance of a set of heights in centimetres comes out in cm². Taking the square root undoes that and returns the standard deviation, a spread you can actually mark on the axis alongside the data. Ronald Fisher coined the word "variance" in a 1918 paper on Mendelian inheritance, precisely because he needed a quantity that partitioned additively across sources of variation; the whole of analysis of variance grew out of that choice.
The common trap is averaging standard deviations. You cannot: if two independent measurements have σ = 3 and σ = 4, the combined spread is √(9 + 16) = 5, not 3.5. Add the variances, then take the root. Numerically the conversion is trivial in both directions — a standard deviation of 12 means a variance of 144, and a reported variance of 6.25 means a standard deviation of 2.5.
Variance and Standard Deviation formula
- = Variance
- = Standard deviation
Missing one of these? Work it out first, then come back
- Variance — Broad-Sense Heritability, Narrow-Sense Heritability
- Standard deviation — Z-Score (Standard Score), Coefficient of Variation