14 questions linked to/from Motivation behind standard deviation?
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### What is the purpose of the standard deviation?

I don't have any knowledge of statistics beyond high school common sense. Why is the standard deviation usually seen in combinatorics textbooks, and why is the standard deviation defined intentionally?...
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### Why are squares chosen as a weighting method for quantifying the deviations from a mean?

Reading about variance and it occurred to me that this squaring business seems to be used many places in statistics. I think I understand that the square is used to help "weight" values which are ...
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### Are there any statistics texts which give both intuition AND justifications for the equations/methods?

Background: I took multiple statistics classes in both high school and college, but nothing I learned ever stuck. The problem is, things like p-tests, the equations for chi-squared/normal ...
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### Why is variance defined this way? [duplicate]

I don't understand why $Var(X) = E((X-\mu)^2)$. It's defined as the "expected value of the square of the deviation of $X$ from the mean" but I don't understand why it couldn't be $E(X-\mu)$ as that ...
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### How to represent uniformity of a surface?

My knowledge of math is very basic, my statistics knowledge is even less. It was suggested to me that I try asking this question here, so here we go: I am developing a software application that will ...
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### Why is variance defined as the expected value of difference squared? [duplicate]

As I understand it, variance of a random variable is defined as follows: $$\text{Var}(X) = \text{E}[(X-\mu)^2]$$ $X-\mu$ is obviously the difference between the value of ...
The common way to think about distance is Minkowski difference with the special case $r=2$. The definition for standard deviation is $\sqrt{\frac{1}{n-1} \sum (x_i - x)^2}$. Both of these definitions ...