Dispersion or standard deviation?

[LagrangeEuler]

In some textbooks $\Delta \hat{x}$ is called dispersion of coordinate $\Delta \hat{x}=(\langle \hat{x^2} \rangle-\langle \hat{x} \rangle ^2)^{\frac{1}{2}}$. For me that is standard deviation. What do you think?

 

[Meir Achuz]

I have never seen 'dispersion of coordinate' used. It strikes me as something translated from English to another language, and then translated back.

 

[jtbell]

"Standard deviation" is the term that I've always used; or for its square, the "variance".

A Google search for "dispersion standard deviation" turns up many pages with statements like "the standard deviation is a measure of dispersion". So "dispersion" is the general idea of "width" of a statistical distribution, and the "standard deviation" is a specific way of describing or measuring it mathematically.

 

[LagrangeEuler]

What name you use for $\Delta \hat{x}$? What is that mathematically for you?