# Dispersion or standard deviation?

1. Mar 22, 2014

### 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?

2. Mar 22, 2014

### 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.

3. Mar 22, 2014

### Staff: Mentor

"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.

4. Mar 22, 2014

### LagrangeEuler

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