Easiest description for **standard deviation** definition is distance from mean (expected value) as shown in this graphical depiction

where all the values fall at *σ* distance within the dotted circle radius. Of course a more real-life situation is shown as

where *σ* is the square root of the following mean

*σ*²* *a.k.a. **variance** is averaged quadratic distances. Explanation:

Distance may have several concepts, in this variance description, **distance** shows “how far” a value is from its population expected value (mean). Quadratic form of this “how far” is