Question

When we calculated the Variance (on the way to Standard Deviation) we computed the difference between what we saw in each case (or in each observation), and the Expected value for all of the observations.

Then, we squared those differences before weighting this element by the probability of actually seeing that observation or scenario.

So, what is the effect (or are the effects) of squaring that value?

Answer 1

The purpose of calculating the standard deviation is to understand the risk or volatility of security of variable.

The value of the variable may be positive or negative. We substruct the mean or expected return of the variable from each occurrence and square them to make the each result as positive and multiply them with probability before we square root the sum of all to get the standard deviation.

Here, we first substract each occurance to get the deviation and square them to them a positive number and finally square root them to make the standard deviation a positive number. We square root them because we square them before and by squaring we eliminate any negative result.