# Linked Questions

14 questions linked to/from Motivation behind standard deviation?
6answers
390 views

### 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 ...
1answer
281 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 ...
0answers
33 views

### 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: \begin{equation} \text{Var}(X) = \text{E}[(X-\mu)^2] \end{equation} $X-\mu$ is obviously the difference between the value of ...
4answers
18k views

### 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?...
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 ...
3answers
3k views

### 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 ...
2answers
131 views

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 ...
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 ...
3answers
596 views

### 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 ...
2answers
94 views

### 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 ...
1answer
582 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 ...