Variance

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PAS

Cegep/2

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123 words

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Measure of variability
Special case of covariance in which the two variables are identical

Sample variance:

s^{2} = \frac{\sum_{i = 1}^{n} (x_{i} - \overset{―}{x})^{2}}{n - 1}

Population variance:

σ^{2} = \frac{\sum_{i = 1}^{n} (x_{i} - μ)^{2}}{N}

For discrete classes:

s^{2} = \frac{\sum_{i = 1}^{c} n_{i} (x_{i} - \overset{―}{x})^{2}}{n - 1}

For continuous classes:

s^{2} = \frac{\sum_{i = 1}^{c} n_{i} (c_{i} - \overset{―}{x})^{2}}{n - 1}

Properties

V a r (X) = E (X^{2}) - E^{2} (X) = \sum x^{2} p (x) - {(\sum x p (x))}^{2}

For linear transformation:

V a r (Y) = V a r (a X + b) = a^{2} V a r (X)

For independent variables:

V a r (T) = V a r (X \pm Y) = V a r (X) \pm V a r (Y)

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