Standard Deviation

What is it?

Standard deviation is a statistical measurement mainly used in Descriptive Statistics and Probability, being commonly referenced as $\sigma$. It’s a measure of how dispersed the data is in relation to the mean. Lower standard deviations represent more clustered data, and higher means it’s spread out.

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Calculating the standard deviation

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:

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

Standard deviation vs Variance

One may notice that the formula for standard deviation is quite similar to Variance. In fact, standard deviation can be interpreted as the square root of the Variance of the variable.