[Math] Determine “average min and max” of a list of values

averagestatistics

I've got a large dataset of about 1,000 values which represent the flex of a finger (higher s more flexed). The data is collected within 10 seconds. During that time the finger will be repeatedly flexed and made straight.

I need to find the "average range" meaning that I don't need the global minimum and global maximum but the "average minimum and maximum".

I want to use this "average minimum and maximum" to calculate a normalised finger flex which works independently from the absolute flex value.

How can I do that?

Best Answer

It is not possible to give an optimal answer to your question without definitions of terminology 'normalized finger flex' and 'absolute finger flex'. (These are not terms immediately clear to a statistician, and I am curious about the 'independence' you mention.) What do these two terms mean in terms of finger flexing and why are they important to you?

Also, it would be helpful to see what the data look like: are neighboring values in the sequence of 1000 near to each other (for instance, suggesting a sinusoidal curve), and about how many finger flexes are there in a 10-second period.

Lacking this information I have to guess, and the results of guessing may not be useful to you. It is a little like asking a physician to diagnose a disorder if you say on the phone, "Sometimes the twitch in my left eye is very disturbing."

If the data move fairly regularly up and down about 10 times in 10 seconds, then you might look for several highest local maxima (about 10) and average, and to look for several lowest local minima and average them. Do individual flexes result in widely different max and min values? Do you want to average over all individual flexes, or only get averages for the several most extreme. (By any definition, there would be ways to automate this search pretty well, so after deciding an a strategy by by looking at a couple of data streams of 1000, you could have a computer search additional such streams.)

Another approach (simpler, more general, possibly less satisfactory) would be just to average the top 50 values (about) to get the 'average global maximum' and similarly for the bottom 50 to get the 'average global minimum'. (Of course, "50" is a mildly educated guess without seeing the data.)

The reason I'd like to know what you mean by 'absolute flex value' and how you derive that from data, is that your word 'independent' indicates you want the 'normalized finger flex' to carry fundamentally different information than the 'absolute flex value' and I cannot be sure that is true without knowing what 'absolute flex' means.

If this answer sets you on the right track, then please so indicate. If not, please leave a Comment with more information, and maybe I (or someone else) can do better.

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