Thank you very much for going out your way to do this explanation. It’s something that’s bugged me for a while and I’ve not found a good explanation behind it.
I’m assuming based on this then the median often offers a better “reasonable” person in a given demographic and includes everyone, over mean with top and bottom excluded.
And obviously from your explanation median makes wealth comparisons between nations more accurate.
Well, median, mean and mode are all imperfect, but mean is by far the most imperfect because it ignores the distribution of values per data point (so in this case the distribution of wealth per individual) whilst median and mode do not and so tend to fall towards an indicative value (i.e. wealth level) around were the majority of cases are.
By the way, I made a mistake in my previous post and wealth is not a “normal distribution”, though it is similar.
A normal distribution looks like this but the wealth distribution is not balanced on both sides since the upper tail of cases (i.e. the richer) is theoretically unbound, whilst the lower tail of cases is either bound (at $0 if debt is not included) or only goes up to a certain point if debt is included (basically only up to the point were people will lend money to other people).
Normal distributions (so, the Mathematical, perfectly balanced ones) have amongst other things the property that mean = median = mode so if wealth was a perfect normal statistical distribution then using the mean would not be a problem.
Thank you very much for going out your way to do this explanation. It’s something that’s bugged me for a while and I’ve not found a good explanation behind it.
I’m assuming based on this then the median often offers a better “reasonable” person in a given demographic and includes everyone, over mean with top and bottom excluded.
And obviously from your explanation median makes wealth comparisons between nations more accurate.
Well, median, mean and mode are all imperfect, but mean is by far the most imperfect because it ignores the distribution of values per data point (so in this case the distribution of wealth per individual) whilst median and mode do not and so tend to fall towards an indicative value (i.e. wealth level) around were the majority of cases are.
By the way, I made a mistake in my previous post and wealth is not a “normal distribution”, though it is similar.
A normal distribution looks like this but the wealth distribution is not balanced on both sides since the upper tail of cases (i.e. the richer) is theoretically unbound, whilst the lower tail of cases is either bound (at $0 if debt is not included) or only goes up to a certain point if debt is included (basically only up to the point were people will lend money to other people).
Normal distributions (so, the Mathematical, perfectly balanced ones) have amongst other things the property that mean = median = mode so if wealth was a perfect normal statistical distribution then using the mean would not be a problem.