Is there any specific meaning of the formula 2*(max-min)/(max+min)? I'm a student who studies machine learning.
When I studied this paper(https://dl.acm.org/doi/pdf/10.1145/335191.335388),
I saw the following formula and explanation.
$$(direct_{max} - direct_{min})/direct_{mean} = (indirect_{max} - indirect_{min})/indirect_{mean}$$
The $direct_{mean}$ is the mean value of $direct_{max}$ and $direct_{min}$.
And $indirect_{mean}$ is also the mean value of $indirect_{max}$ and $indirect_{min}$.
In this case, that paper said the fluctuate amount is the same between direct and indirect.
But I don't understand one thing.
Is there any specific meaning of the below formula?
$$2* (value_{max} - value_{min})/(value_{max} + value_{min})$$
I don't know why it has the meaning as the amount of fluctuating.
Thank you for reading my question.
 A: You can rewrite the formula as follows:
$$ \frac{2*(\text{Max}-\text{Min})}{\text{Max}+\text{Min}} $$
$$ = \frac{\text{Max}-\text{Min}}{\frac{\text{Max}+\text{Min}}{2}} $$
$$ = \frac{\text{Range}}{\text{AVG(Min, Max)}} $$
The numerator is the range, and the denominator is the average of the max and min. You can think of that numerator as a measure of spread, and the denominator as a measure of central tendency. So, this ratio is similar to other dimensionless/normalized metrics that measure noise/signal, like $\frac{\sigma}{\mu}$ or $\frac{\text{IQR}}{\text{Median}}$.
EDIT: As noted in comments on the original question, this is a rough normalized measure of spread unless we know a lot more about the distribution. If the distribution of observed values is approximately symmetric and unimodal, then that average is likely close to the mean or median. But, if the distribution is skewed or multimodal, then the average of the min and max can be wildly different from most actual observations.
