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I have RGB brightness values over a possible range of 1-255. I am already computing Coefficient of Variation, but since my domain is strictly limited, I am interested in seeing a measure of how spread out a given channel's values are over the domain.

I am considering getting Std Dev over 254 or possibly p-range over 254. (You may detect I am weak in statistics.) Is there any standard measurement for this kind of situation, and what is it called?

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    $\begingroup$ Standard deviation makes no assumptions about range of the variable. $\endgroup$
    – Tim
    Commented Apr 19, 2019 at 15:14
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    $\begingroup$ What are you going to use this statistic for? $\endgroup$
    – Peter Flom
    Commented Apr 19, 2019 at 15:15
  • $\begingroup$ I am seeking patterns in aerial imagery develop algorithms to brighten pixels in shadows to be of similar brightness as their near neighbor pixels in direct sunlight. Also, many areas in shadow have similar means with still water in direct sunlight, so I want to see if there is a way to separate those. I am in an early phase of this work, seeking approaches that can discriminate among types. $\endgroup$
    – philologon
    Commented Apr 19, 2019 at 15:21
  • $\begingroup$ Depending on your needs, the standard deviation may be more useful than the coefficient of variation. I would think in this case that the absolute differences are more interesting than the relative differences. You may also be interested in a transformation like $y = \frac{x}{(x+0.5)(255.5-x)}$ to stretch the range endpoints. You may also want to take a look at the InterQuartile Range. [Edited comment.] $\endgroup$
    – Ertxiem - reinstate Monica
    Commented Apr 19, 2019 at 15:25
  • $\begingroup$ Just a small detail: if it's an RGB colour code, then the minimum is $0$ unless you have some type of restriction. And, by the way, you can use MathJax to write the range as $[0; 255]$. $\endgroup$
    – Ertxiem - reinstate Monica
    Commented Apr 19, 2019 at 15:25

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Maybe you can consider calculating entropy. It is a better tool for representing the variation of binned data like a RGB image.

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