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An “average” (whether a mean/ median etc) is a very lossy compression algorithm. You’re attempting to describe a whole series of numbers with just one (or two)
by LeonB 1y ago
An “average” (whether a mean/ median etc) is a very lossy compression algorithm.
You’re attempting to describe a whole series of numbers with just one (or two) numbers.
Trying to come up with a good general purpose way to reduce/compress/aggregate data via a lossy algorithm is intractable.
While that all might sound obvious, it can be very hard to internalise this.
(And that’s before getting into the motivated reasoning that biased actors [aka normal people] will use to preference one lossy algorithm over another)
- amelius 1y agoYou can use an increasing number of statistical moments. https://en.wikipedia.org/wiki/Moment_(mathematics) https://en.wikipedia.org/wiki/Moment_(mathematics) The arithmetic mean is one of them, which would be an argument in favor of it.
- john-h-k 1y agoI don't think it is an argument in favour of it. arith-mean = E[x] , the first moment of x geo-mean = exp(E[log x]) , so log geo-mean = first moment of log x They are both equivalent in amount of information preserved, but arithmetic preserves additive structure whereas geo preserves multiplicative structure
- amelius 1y agoI didn't want to imply that there is a loss of information. Yes, it's one level up in the hyperoperation chain, I suppose, but what I meant is that it's not a typical way of doing statistics, especially the higher moments.