Articles of standard deviation

Determining variance from sum of two random correlated variables

I understand that the variance of the sum of two independent normally distributed random variables is the sum of the variances, but how does this change when the two random variables are correlated?

incremental computation of standard deviation

How can I compute the standard deviation in an incremental way (using the new value and the last computed mean and/or std deviation) ? for the non incremental way, I just do something like: mean = Mean(list) for i = 0 to list.size stdev = stdev + (list[i] – mean)^2 stdev = sqrRoot( stdev / […]

Correctness of a statistical evaluation of a parameter

I have a question about a non-Gaussian distributed parameter that can only take certain values in a defined interval. Knowing that I have to define this parameter starting from a set of its values and in the end I must use only average value and tolerance, I am asking myself if the mean value should […]

Why the standard deviation of the sample mean is calculated as $\frac{\sigma}{\sqrt{n}}$?

According to Wikipedia, the standard deviation of a sample mean is calculated as follows $$\frac{\sigma}{\sqrt{n}}$$ Why is that? Why do we need to divide the standard deviation of the population by the square root of $n$ (which should I think be the size of the sample)? Why should that make sense?

Variance is the squared difference – why not to the 3, or 4 instead?

So there is this question about why variance is squared. And the answer seems to be “because we get to do groovy maths when it is squared“. Ok, that’s cool, I can dig. However, I’m sitting reading some financial maths stuff, and a lot of the equations on pricing and risk are based on variance. […]

Why is variance squared?

The mean absolute deviation is: $$\dfrac{\sum_{i=1}^{n}|x_i-\bar x|}{n}$$ The variance is: $$\dfrac{\sum_{i=1}^{n}(x_i-\bar x)^2}{n-1}$$ So the mean deviation and the variance are measuring the same thing, yet variance requires squaring the difference. Why? Squaring always gives a positive value, so the sum won’t be zero, but absolute value also gives a positive value. Why isn’t it $|x_i-\bar […]

Why is there not a simpler way to calculate the standard deviation?

Steps of getting standard deviation. Work out the average (mean value) of your set of numbers Work out the difference between each number and the mean Square the differences Add up the square of all the differences Divide this by one less than the number of numbers in your set – this is called […]

Why do statisticians like “$n-1$” instead of “$n$”?

Does anyone have an intuitive explanation (no formulas, just words! :D) about the “$n-1$” instead of “$n$” in the unbiased variance estimator $$S_n^2 = \dfrac{\sum\limits_{i = 1}^n \left(X_i-\bar{X}\right)^2}{n-1}?$$

Recursive formula for variance

I’d like to know how I can recursively (edit: iteratively) compute variance, so that I may calculate the standard deviation of a very large dataset in javascript. The input is a sorted array of positive integers.

How can I calculate “most popular” more accurately?

I’m developing a website at the moment. The website allows users to “rate” a post from 0 to 5. Posts can then be displayed in order of popularity. At the moment, my method of calculation is pretty primitive: average_rating = total_rating/ratings the problem is that a story with 1 rating of 5 is more popular […]