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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### 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 $\sqrt{\frac {\sum(x-\mu)^2} {N}}$ 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 ...
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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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### 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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### Where do the definitions in statistics come from? [duplicate]

The most statistics I ever took was a few lessons on it back in high school. What always bothered me is how arbitrary the definitions seemed. For instance, I remember having trouble with the ...
Mean Squared Error: $\operatorname{MSE}=\frac{1}{n}\sum_{i=1}^n(\hat{Y_i} - Y_i)^2.$ <-- what is the purpose of the '$^2$' in here? Mean Absolute Error: $\mathrm{MAE} = \frac{1}{n}\sum_{i=1}^n \... 2answers 7k views ### How can I tell if dice are biased or unbiased, given a number of trials? If I'm given the outcome of a number of dice rolls (say, 5 twos, 8 threes, etc), is there a way to assign a probability that the dice are biased or unbiased? If so, how? Or alternatively, how can I ... 1answer 148 views ### Are there any statistics texts which give both intuition AND justifications for the equations/methods? Background: I took multiple statistics classes in both high school and college, but nothing I learned ever stuck. The problem is, things like p-tests, the equations for chi-squared/normal ... 1answer 269 views ### Why is variance defined this way? [duplicate] I don't understand why$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)$as that ... 1answer 579 views ### How to represent uniformity of a surface? My knowledge of math is very basic, my statistics knowledge is even less. It was suggested to me that I try asking this question here, so here we go: I am developing a software application that will ... 1answer 76 views ### What is The Basis for The Similarity Of Distance And Standard Deviation? The common way to think about distance is Minkowski difference with the special case$r=2$. The definition for standard deviation is$ \sqrt{\frac{1}{n-1} \sum (x_i - x)^2}$. Both of these definitions ... 0answers 89 views ### Why the definition of Variance is such. [duplicate] Why we define the variance of a random variable$X$as$\text{var}[X]=\text{E}[(X-\mu)^2]$instead of$\text{var}[X]=\text{E}[\left|X-\mu\right|]$. Normally we understand the standard deviation$\...
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 ...