Variance

Description

Variance is a statistical measure that quantifies the amount of variation or dispersion of a set of data points around its mean (average) value. It essentially indicates how spread out the data is.

A higher variance suggests that the data points are more scattered, while a lower variance indicates that the data points are clustered closer to the mean.

Info

High variance is better than low variance because that feature carries more meaning, as long as it’s meaningful and not just outliers.

Formula

The variance is the average value of the squared difference between the random variable and its expectation

\[ \text{Var}(X) = E[(X - E[X])^2] \]

Or in other shape:

Variance is the expectation of the squared deviation of a random variable from its population mean or sample mean.

\[ S^2 = \frac{\sum{(x_i - \bar{x})^2}}{n - 1} \]

\(S^2\) = sample variance
\(x_i\) = the value of one observation
\(\bar{x}\) = the mean value of all observations
\(n\) = the number of observations

Vs Mean

The mean is the average of a group of numbers, and the variance measures the average degree to which each number is different from the mean.