Things like wealth and income (and alcohol consumption) don’t even have useful mean. They’re monotonically decreasing distributions with most people scoring near 0 and a few people scoring extremely high. It’s more like an exponential distribution than a gaussian.
In the US, mean household wealth is something like 3-4x the median, and if you plug the numbers into the standard deviation formula, you’ll get something close to the mean. Even greater. Maybe that informs a very sophisticated statistician audience, but if you tell the general public ‘standard deviation,’ they think “63% of people are within that of the mean,” and that is only true of Gaussian. For exponential distribution, mean±SD gets approximately all the samples.
Wouldn’t it still tell you how concentrated the data are around the mean? Just not as reliably as for a gaussian distribution.
Things like wealth and income (and alcohol consumption) don’t even have useful mean. They’re monotonically decreasing distributions with most people scoring near 0 and a few people scoring extremely high. It’s more like an exponential distribution than a gaussian.
In the US, mean household wealth is something like 3-4x the median, and if you plug the numbers into the standard deviation formula, you’ll get something close to the mean. Even greater. Maybe that informs a very sophisticated statistician audience, but if you tell the general public ‘standard deviation,’ they think “63% of people are within that of the mean,” and that is only true of Gaussian. For exponential distribution, mean±SD gets approximately all the samples.
TYVM!