I have a colleague who sent me an Excel spreadsheet where she added up the values of the natural logs [=LN(x)] of several numbers and then divided by the number (count) of logs to get the “average” natural log.
But when you add natural logs together, aren’t you really multiplying them?
The number in the numerator would be the product, not the sum, right?
Is this valid, and if not, how would you get the “average” natural log of a number of logs?
Do you need to find the geometric mean and not the arithmetic?
When you add logs, you’re multiplying their arguments. Averaging the logs and taking the exponent is like multiplying the arguments of the logs and taking the nth root if there were n of them. That is a geometric mean.
So, averaging logs will give you the log of the geometric mean of all their arguments.
It is perfectly valid, assuming that result is the one you wanted.
In fact, this is probably how your favorite geometric mean routine calculates geometric means. Multiplying together a lot of numbers puts you at serious risk for overflow or underflow, but averaging together their logs and taking the exponential doesn’t.
