Calculating Average Fluctuation

[Phyisab****]

Homework Statement

I have been asked find the average fluctuation in a certain value. But I don't know what that means. Say x fluctuates about a mean.

$$(\overline{(\Delta V)^{2}})^{1/2}?$$

But that's the root mean square fluctuation, which isn't the same. Then how about

$$\overline{\Delta V}$$

now that's the average fluctuation right?
But if I only know the average value, and the root mean square fluctuations, then how can I find the plain old average fluctuation from that?

 

[jbsteele]

Homework Equations No equations given. The Attempt at a SolutionIf you know the average value and the root mean square fluctuations, then you can use the following formula to calculate the average fluctuation: \overline{\Delta V} = (\overline{(\Delta V)^{2}})^{1/2} / sqrt(N)where N is the number of samples used to calculate the average and root mean square fluctuations.

 

[kerimek]

The average fluctuation refers to the average deviation of a certain value from its mean value. In other words, it is the average difference between the value and its mean. This can be calculated by taking the average of the absolute values of all the fluctuations, or by taking the root mean square fluctuation and dividing it by \sqrt{2}. So, to find the plain old average fluctuation, you can use the formula:
\overline{\Delta V} = \frac{1}{N}\sum_{i=1}^{N}|(x_i - \overline{x})| = \frac{(\overline{(\Delta V)^{2}})^{1/2}}{\sqrt{2}}
where N is the total number of fluctuations and x_i is the individual fluctuation. This will give you the average fluctuation in the same units as the original value.