14 questions linked to/from Motivation behind standard deviation?
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### probability variance formula intuition [duplicate]

Here is the formula for the variance : $\sigma^2=\dfrac{\sum(X-\mu)^2}{N}$. My question is why do we SQUARE the difference between the mean and the variable, why don't we use absolute value ...The ...
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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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### 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 ...
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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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### What is The Basis for The Similarity Of Distance And Standard Deviation?

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 ...
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### In calculating the standard deviation, why do we square the difference from the mean, as opposed to cubing? [duplicate]

This question has been bothering me for a while: In calculating the standard deviation, why do we square the difference from the mean, as opposed to cubing the differences (and then taking the cube ...
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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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### How can I tell if dice are biased or unbiased, given a number of trials?

If I'm given the outcome of a number of dice rolls (say, 5 twos, 8 threes, etc), is there a way to assign a probability that the dice are biased or unbiased? If so, how? Or alternatively, how can I ...
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### Why $\sqrt{\frac {\sum(x-\mu)^2} {N}}$ instead of $\frac {\sum{\Bigl|x-\mu\Bigr|}} {N}$? [duplicate]

Possible Duplicate: Motivation behind standard deviation? In statistics very often you see something of the sort: $$\textrm{quantity}=\sqrt{\frac {\sum(x-\mu)^2} {N}}$$ to measure things like ...