John Allen Paulos on the mean and the median

In an ABC news commentary, he points out something that is easily mathematically demonstrable[1], but isn’t necessarily noticed by the general public: the difference between the mean and the median.

The Republican spin machine has been carefully misusing the mean to say that the economy is improving, because (using 2004’s numbers) mean income is up; however, the median is down. The increase in incomes at the high end brought the mean up, but that’s only because the richest 1% had their incomes grow by almost 17%.

Even within that small group, there’s a lot of inequality. Half of the increase in income going to the top 1% of households went to the top 0.1%….

This is why the Republicans will only raise the minimum wage if they can cut the estate tax.

[1] You live in a town of 10 people. Last year: eight of you had incomes of $20K, one made $10K, and the tenth person wound up with $90K. The mean income was $26K, but the median was $20K.

This year: the $10K person lost his job and made $5K at a part-time job, six of the eight lost hours at their jobs and made $15K each, two folks managed to keep their salaries where they were at $20K, and Thurston Gateston IV over there made $150K. Mean (per capita) income? $28.5K! Hey, that’s a huge increase, over 42% higher than last year! Ignore the fact that the median dropped from $20K to $15K, and the economy looks great. (If you’re Thurston, it is; his income increased by 67%.)

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