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> But because the income distribution is such that the median income is greater than its simple arithmetic average, the median income of taxpayers who left San
by carbocation 4y ago
> But because the income distribution is such that the median income is greater than its simple arithmetic average, the median income of taxpayers who left San Francisco would probably have been around $250,000.
What? That would be extremely unusual, if true. (The long tail on the upper end is unbounded, while on the lower end income is bounded at 0. So for income, usually mean >>> median.)
Did they get mean and median reversed?
= = = = =
Edit I drew a random sample of incomes for 1,000 people (between $0 and $1 million) and used Pytorch to update these incomes to achieve mean $196,000 and median $250,000. (I also heavily penalized income < $0.)
The shape of the distribution of incomes to achieve such a feat, as one would predict, is absurd. X axis is income in $, Y axis is the number of people with that income out of 1,000. (First image.)
If instead the economist got his understanding of mean and median reversed, you get the second image, which is zero-inflated but otherwise uniform in income.
https://imgur.com/6OiIF3V https://imgur.com/6OiIF3V
- zeroonetwothree 4y agoThis article is written by a "Professor of Economics" too. Indeed in SF average household income is $167k while median is $120k.
- CamperBob2 4y agoHe's talking specifically about the people who left, not the people who are still there.
- carbocation 4y agoThe fact that the lower end of income is bounded—while the upper end is not—is true for both groups.
- kingkawn 4y agoThis is like the old saying, “The law, in its majestic equality, forbids rich and poor alike to sleep under bridges, to beg in the streets, and to steal loaves of bread.”
- zeroonetwothree 4y agoNo, he is speculating about the people that left based on the general distribution: > But because the income distribution is such that the median income is greater than its simple arithmetic average, the median income of taxpayers who left San Francisco would probably have been around $250,000.
- jrumbut 4y agoI'm sympathetic to the argument that there might be something unusual about the income distribution of the people who left San Francisco for various ski resort towns but pulling a very specific number like $250k out of the air is weird. The silliest part is that it doesn't change the argument. $196k is a good income, $250k is better but not qualitatively different by any means.
- jmeister 4y agoIt is not pulled out of thin air. It's Stanford/Hoover, if they have access to the mean they have access to the median, probably more fine grained data too.
- jrumbut 4y agoYou would think that, but the article text says otherwise: > the median income of taxpayers who left San Francisco would probably have been around $250,000. I am as puzzled as you, why not just calculate the median or email the people with the data and ask for it? Otherwise it feels like reaching for anything to embellish a partisan talking point.
- jmeister 4y agoNo it's just about skew. https://openstax.org/books/introductory-business-statistics/pages/2-6-skewness-and-the-mean-median-and-mode https://openstax.org/books/introductory-business-statistics/...
- carbocation 4y agoSkew is fundamental to my point.