3 ms·

It so happens that the most useful number is usually the dominant (also known as mode or most common value), which is not visible on the histogram, especially f

It so happens that the most useful number is usually the dominant (also known as mode or most common value), which is not visible on the histogram, especially for flat heavy tailed distributions such as income these days.

thaumasiotes 4y ago
> the most useful number is usually the dominant (also known as mode or most common value), which is not visible on the histogram Are you kidding? It's the highest point on the histogram; a histogram places very heavy visual emphasis on the mode while obscuring the mean and median.
- AstralStorm 4y ago
  Sometimes true, but it is the only value that can be estimated without error in some cases. Neither median nor average is useful for a central tendency in a weird distribution - and income tends to be one. Histograms typically bucket data potentially hiding the true value of mode or adding error to it. It really should be given directly, with a count of occurences. Mode is not the same as modal class - which is what you would get from a histogram.
  - thaumasiotes 4y ago
    > Histograms typically bucket data potentially hiding the true value of mode or adding error to it. It really should be given directly I can't agree with that. It is true that histograms bucket data. But the width of the buckets is chosen to make sense in context. It just isn't relevant if people making $20,176 slightly outnumber people making $20,359. So we put them in the "$15,000 - $24,999" bucket, which preserves most of the information of interest while omitting the information that is of absolutely no interest. In other contexts, you see other bucket widths. Chinese university entrance exam scores are published with a bucket width of one point. (Some things may be obscured. When I was looking into this, I found that it was very common for the top scores to be bucketed with each other, presumably for some kind of privacy reasons. Beijing was notable in putting low scores into buckets of width ten even in what was technically labeled an 一分一段表 (literally: "one point -- one section" table). Fujian was notable the other way, for preserving the bucket width of one point even for the highest scores; I have trouble believing it's a coincidence that Fujian is one of the academically highest-performing regions of China.) > Mode is not the same as modal class - which is what you would get from a histogram. For almost all purposes, modal class is more interesting, more useful, and more statistically valid than raw mode is.
notahacker 4y ago
Individual incomes seem like one of those areas where that isn't the case. The modal individual income is likely 0 for most countries (economically inactive people), but the earnings of the people the economically inactive are dependent on will vary hugely.

thaumasiotes 4y ago

> the most useful number is usually the dominant (also known as mode or most common value), which is not visible on the histogram Are you kidding? It's the highest point on the histogram; a histogram places very heavy visual emphasis on the mode while obscuring the mean and median.

AstralStorm 4y ago
Sometimes true, but it is the only value that can be estimated without error in some cases. Neither median nor average is useful for a central tendency in a weird distribution - and income tends to be one. Histograms typically bucket data potentially hiding the true value of mode or adding error to it. It really should be given directly, with a count of occurences. Mode is not the same as modal class - which is what you would get from a histogram.
- thaumasiotes 4y ago
  > Histograms typically bucket data potentially hiding the true value of mode or adding error to it. It really should be given directly I can't agree with that. It is true that histograms bucket data. But the width of the buckets is chosen to make sense in context. It just isn't relevant if people making $20,176 slightly outnumber people making $20,359. So we put them in the "$15,000 - $24,999" bucket, which preserves most of the information of interest while omitting the information that is of absolutely no interest. In other contexts, you see other bucket widths. Chinese university entrance exam scores are published with a bucket width of one point. (Some things may be obscured. When I was looking into this, I found that it was very common for the top scores to be bucketed with each other, presumably for some kind of privacy reasons. Beijing was notable in putting low scores into buckets of width ten even in what was technically labeled an 一分一段表 (literally: "one point -- one section" table). Fujian was notable the other way, for preserving the bucket width of one point even for the highest scores; I have trouble believing it's a coincidence that Fujian is one of the academically highest-performing regions of China.) > Mode is not the same as modal class - which is what you would get from a histogram. For almost all purposes, modal class is more interesting, more useful, and more statistically valid than raw mode is.

notahacker 4y ago

Individual incomes seem like one of those areas where that isn't the case. The modal individual income is likely 0 for most countries (economically inactive people), but the earnings of the people the economically inactive are dependent on will vary hugely.