Alright, this is rooted in a confusion between the normal use in statistics and the normal use in human speech.
Absolutely, average-without-qualifications means the mean, if we're going to be handed a list of actual numbers and expected to produce another number from them.
But especially for highly right-tailed distributions, when people talk about the average, they mean something more like the median, if there's a significant difference.
I would find it annoyingly pedantic if someone said the average net worth in Jeff Bezos' municipality was 60mm, if the median was closer to 0.75mm. If I was handing someone an Excel spreadsheet of tax returns, I would of course tell them that we needed the median. Or the mean but in this circumstance I wouldn't use the word 'average' because of the wide skew. If I did anyway, yeah I would probably get the mean back.
That's how average works in statistics, but not in common speech.
Alright, this is rooted in a confusion between the normal use in statistics and the normal use in human speech.
Absolutely, average-without-qualifications means the mean, if we're going to be handed a list of actual numbers and expected to produce another number from them.
But especially for highly right-tailed distributions, when people talk about the average, they mean something more like the median, if there's a significant difference.
I would find it annoyingly pedantic if someone said the average net worth in Jeff Bezos' municipality was 60mm, if the median was closer to 0.75mm. If I was handing someone an Excel spreadsheet of tax returns, I would of course tell them that we needed the median. Or the mean but in this circumstance I wouldn't use the word 'average' because of the wide skew. If I did anyway, yeah I would probably get the mean back.
That's how average works in statistics, but not in common speech.