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.
Statistical Variance - dCode
Tag(s) : Statistics
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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.
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). $$ V(X) = \mathbb{E} \left[(X - \mathbb{E}[X])^{2}\right] $$
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 \( V = \frac{1}{3-1} \left( (1-4)^2 + (2-4)^2 + (9-4)^2 \right) = 38/2 = 19 \)
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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