Variance debunked tutorial

When learning statistics, one of the most fundamental yet usually grossed over concepts is that of variance (i.e. the square of the standard deviation in normal distribution).

As we know, virtually all statistical operations which measure deviations of individual values from the norm involve adding the SQUARED differences between the two numbers. However, very few instructors could explain why we have to use squares rather than just the absolute values of the difference (or other even powers such as 4, if the intention is to avoid the negatives). This tutorial shall cover this in a convincing manner.

Secondly, while we all know the variance of a SAMPLE is arrived by dividing (n-1) of the sum of squared differences, where n is the number of observations, few can articulate the rationale behind it. This tutorial shall also prove step by step why this is case, so after this you could appreciate the logic behind this ingenious insight instead of just reciting it like a medieval myth.