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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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.

Answers to Questions

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: $$ V(X) = \sigma^{2}(X) $$

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