Average of power curve functions

Labyrinth

I have a program that generates a bunch of power curve functions and would like to know what the 'average' function between all of them would be.

Here is my data set so far:

4.638013x^0.076682586
4.834884x^0.034875062
4.0432342x^0.13476002
3.8535004x^0.12178477

How do I do this, and what is the average function for this particular set?

Thank you for your time.

SteamKing

Staff Emeritus
Homework Helper
It depends on what you mean by 'average'.

Labyrinth

I think the mean would be ideal.

I'm looking at it from a graph standpoint, where I want to find one curve that best represents them all.

Mark44

Mentor
I would lean toward taking the average of the four coefficients (the numbers in front of the power functions), and the average of the four exponents. That would certainly give you a function whose graph would be somewhere in the middle of the other four.

Labyrinth

Is it really that simple? I guess I had delusions of complexity.

Anyways thanks for your help.

Stephen Tashi

Is it really that simple?
The un-simple task you have not done is to figure out precisely what you are trying to accomplish. What do you intend to use this "average" function for?

Labyrinth

The un-simple task you have not done is to figure out precisely what you are trying to accomplish. What do you intend to use this "average" function for?
I'm attempting to approximate the faulty motion reporting of a mouse sensor in terms of a power curve which it doesn't really follow but is available to mimic in settings available with many interfaces that support acceleration. The data I get is a bit noisy, so I take a sample, approximate its curve with a graphing program, take another sample, approximate that one, and so on. Over many iterations the 'average' function between them all should be a reasonable approximation.

There's a definite limit on the precision as long as only a simple power curve is available. It's more precisely described as a higher order polynomial. At a later date I may get into its exact description in these terms but for now a simple power curve takes priority.

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