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?

 

[blue_raver22]

I understand that terminology can vary in different fields and contexts. However, in the context of statistics and probability, the term "standard deviation" is commonly used to describe the measure of dispersion or variation of a set of data from its mean. In this case, the formula for dispersion of coordinate $\Delta \hat{x}$ is equivalent to the formula for standard deviation. Therefore, I would agree with your interpretation that $\Delta \hat{x}$ can be referred to as standard deviation in this context.