Variance

What is it?

Variance is a statistical measurement, mainly used in Descriptive Statistics. Variance measures how far each data point is from the mean, which can be interpreted as the average squared error to the mean.

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Calculating the variance

Given $x$ as the variable, $\overline{x}$ as the mean value of the variable, and $n$ as the total number of data points, one can apply the following formula to get the standard deviation of a variable:

$$\begin{array}{rl}& \text{For populations:}\\ & {\sigma }^2=\frac{\sum (x_i-\overline{x}{)}^2}{n}\\ & \\ & \text{For samples:}\\ & s^2=\frac{\sum (x_i-\overline{x}{)}^2}{n-1}\end{array}$$

Variance vs Standard deviation

The formula used for variance can be thought as one of the steps to calculate the Standard Deviation. In fact, variance can be interpreted as the squared Standard Deviation.