I was thinking what the dispersion of a normal distribution is wo much knowledge and it is the weighed average distance (squered) for points respect to the mean. Squared to remove sign cancellation.
If this is the case, there should be something like an integration of the formula $g*(mean-x)^2$ where $x$ is the variable we measure (the x axis) and may go between -+infinity. If it is normally, mean will indeed be 0.
And $g$ is the Gauss frequency formula.
However I do not find much in google, maybe because I do not know the right terminology.
- Is the basic idea of $g*(mean-x)^2$ conceptually correct?
- How would you derive the formula for the dispersion?
- Do you find the derivation somewhere?
You are essentially describing the variance of the normal distribution. This is one of the two parameters that define the normal distribution - $\mathcal{N}(\mu, \sigma^2)$ is a normal distribution with mean $\mu$ and variance $\sigma^2$. For the standard normal distribution $\mathcal{N}(0, 1)$ the mean is zero and the variance is 1.