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libertangoSince he's exercised his right to ignore my previous emails to him when he makes this kind of mistake... {shrug}
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Jerry:
Re your comments about the danger of Bill Gates to the school system -- when you say, "half the children are below average," this is mathematically incorrect. Half the children are below median. The proportion above or below average will vary according to the sample.
Quick example: If you, I, and Bill Gates walk into a bar the average net worth is going to be somewhere around $20 billion (per Forbes in 2008). But the median net worth (I'll take a wild guess here) will be somewhere around a million.
Two thirds of the sample is "below average" -- not half.
This means that when Keillor speaks of the parents in Lake Wobegon (note the spelling) thinking that all their kids are above average, he's actually making a sophisticated mathematical joke. One is that, as you show in your essay here, the audience misunderstands the concept of average, and will therefore laugh at what they believe to be the parents' vanity. But while they may be vain, they may not. It's entirely possible that there's one kid in town so stupid all the other kids are above average.
When it comes to your perceived adversaries I would make a comment about motes and beams, but perhaps that would be too cruel.
-- Hal O'Brien
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UPDATED TO ADD:
* This article in the New York Times makes the same mistake citing one David Gale of UC Berkeley, on the topic of average number of sexual partners. Slate took it to task, as did others.
* Making the example more extreme: If Bill Gates walks into a room with a 1000 people, the average net worth will be about $60 million. Unless the audience is pre-selected, my guess is 950 of those 1000 would be "below average." So, yes, this really can scale.
FURTHER UPDATED:
* This bio page (which has the whiff of a handout) says Jerry's academic background is, "Bachelors in Psychology and Mathematics, his Masters in Experimental Statistics and Systems Engineering, and his Doctorates in Psychology and Political Science." So he knows the difference. He just chose to ignore it because those tricksy facts got in the way of his polemical point.
*^*^*
Jerry:
Re your comments about the danger of Bill Gates to the school system -- when you say, "half the children are below average," this is mathematically incorrect. Half the children are below median. The proportion above or below average will vary according to the sample.
Quick example: If you, I, and Bill Gates walk into a bar the average net worth is going to be somewhere around $20 billion (per Forbes in 2008). But the median net worth (I'll take a wild guess here) will be somewhere around a million.
Two thirds of the sample is "below average" -- not half.
This means that when Keillor speaks of the parents in Lake Wobegon (note the spelling) thinking that all their kids are above average, he's actually making a sophisticated mathematical joke. One is that, as you show in your essay here, the audience misunderstands the concept of average, and will therefore laugh at what they believe to be the parents' vanity. But while they may be vain, they may not. It's entirely possible that there's one kid in town so stupid all the other kids are above average.
When it comes to your perceived adversaries I would make a comment about motes and beams, but perhaps that would be too cruel.
-- Hal O'Brien
*^*^*
UPDATED TO ADD:
* This article in the New York Times makes the same mistake citing one David Gale of UC Berkeley, on the topic of average number of sexual partners. Slate took it to task, as did others.
* Making the example more extreme: If Bill Gates walks into a room with a 1000 people, the average net worth will be about $60 million. Unless the audience is pre-selected, my guess is 950 of those 1000 would be "below average." So, yes, this really can scale.
FURTHER UPDATED:
* This bio page (which has the whiff of a handout) says Jerry's academic background is, "Bachelors in Psychology and Mathematics, his Masters in Experimental Statistics and Systems Engineering, and his Doctorates in Psychology and Political Science." So he knows the difference. He just chose to ignore it because those tricksy facts got in the way of his polemical point.
