Linked Questions

2
votes
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 ...
4
votes
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 ...
2
votes
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 ...
6
votes
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?...
0
votes
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 ...
0
votes
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 ...
2
votes
2answers
131 views

What is the idea behind the $^2$ in the mean squared error?

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 \...
3
votes
2answers
123 views

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 ...
4
votes
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 $\...
5
votes
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 ...
2
votes
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 ...
3
votes
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 ...
5
votes
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 ...
2
votes
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 ...