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Statistical Variance

Tool to calculate the variance of a list of values. Variance is a statistical value that measures the dispersion characteristic of a distribution or sample.

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Statistical Variance -

Tag(s) : Statistics

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Statistical Variance

Unbiased Variance Calculator

Tool to calculate the variance of a list of values. Variance is a statistical value that measures the dispersion characteristic of a distribution or sample.

What is the variance? (Definition)

Variance is a measure of the dispersion of a list of values around its mean. This value, denoted $$V$$ or $$\mathbb{V}$$ or $$\mathrm{Var}$$ characterizes the way in which the data $$X$$ (random variable) are dispersed by measuring the deviations between each value (of the variable) and the mean (or expected value). $$V(X) = \mathbb{E} \left[(X - \mathbb{E}[X])^{2}\right]$$

How to calculate the statistical variance from a list of numbers? (Formula)

From a list of numbers $$x_i$$ of a random variable $$X$$ whose mean is $$m$$ and with an unknown distribution, the formula is $$V(X)= \frac{1}{n-1} \sum_{i=1}^{n}(x_{i}-m)^2$$

Example: The (unbiaised) variance of the set of 3 numbers 1,2,9 with a mean of 4 is $$V = \frac{1}{3-1} \left( (1-4)^2 + (2-4)^2 + (9-4)^2 \right) = 38/2 = 19$$

What is the relation between variance and standard deviation?

The value of the variance is the square of the standard deviation. Knowing the value of the standard deviation $$\sigma$$, $$V$$ can be calculated with the relation: $$V(X) = \sigma^{2}(X)$$