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Mathematical Literacy: Average (Mean) vs Median
by amr
+2 Reply

Saletan says "By definition, the chance that you'll die before your projected life expectancy is 50 percent." This is not true by definition. While most distributions we see in life are nearly symmetrical, so this is true as a general rule, future life expectancy is not such a case. Saletan is confusing "projected life expectancy" (an average) and the median life expatancy.

Consider 6 people age 70. If their future life expectancies are, 3, 7, 12, 13, 20, and 35, their average life expectancy is 15 years. However, their median life expectancy is 12.5 years. This is the age at which the chance of living that long is 50%.

(Note: this is just a exaggerated example to illustrate the difference. I don't have any continuance tables next to me to be able to say what an actual distribution could look like.)

Re: Mathematical Literacy: Average (Mean) vs Median
by Saletan Editor

Ya got me there. I should have said "roughly." But this is pretty commonsensical: The way life expectancy works, the mean-median gap wouldn't be nearly as big at 66 as it is at 0.

Re: Mathematical Literacy: Average (Mean) vs Median
by auros
I dunno, Will. I think it may be nearly as skewed, just in the opposite direction. I think the figures are roughly like: most of us die by 75-80, but a few live to 110. Your population, starting from 65, looks like a big cluster in the range of 5-15, but with a few outliers up in at 30-35. In percentage terms, this is going to create as big a skew as the life expectancy at birth, where the average is being dragged down (from the 70s) by the relatively small number of people who die at 15 or 25 or 35.
Re: Mathematical Literacy: Average (Mean) vs Median
by cypher
Quick, is there an insurance claims adjuster in the house?
Re: Mathematical Literacy: Average (Mean) vs Median
by apropos1
Saletan, maybe you should give up "science writing''. Don't all those tables and peer-reviewed journals make your head hurt? They must because you don't seem to pore over them too often. I'd suggest 'religious writing' over on faith-based or maybe some conservative online mag, that's about up your alley. You're good for a laugh, though, every once in awhile.
Re: Mathematical Literacy: Average (Mean) vs Median
by Jessica23

Wow apropos1. That was kind of excessive, wasn't it? You disagree with one of his calculations and that leads you to insult his intelligence and the intelligence of all religious folk (Yes, contrary to popular belief, there are many thoughtful, intelligent religious people in all walks of life, including science), implying that he and they are some particularly amusing breed of moron? Damn, homey.

(As an aside, I think it's worth remembering that many of the great scientists and mathematicians throughout history were philosophers and theologians as well. Just something to keep in mind before we start patronizing the faithful.) :P

Re: Mathematical Literacy: Average (Mean) vs Median
by auros
Oh, come on. Getting confused between means and medians is one of the classic errors, especially if you're dealing with a measurement that you don't look at all that often. I happened to know offhand that life expectancies are traditionally reported based on means, because my dad is a gerontologist, so I grew up hearing about life expectancy data. But I honestly think it would be more useful to report medians, and in fact that's what you often see in, say, cancer-survival studies -- what percent of people survive to 1, 5, and 10 years after treatment. (And if you go to the full data tables, you can figure out median survival time and the overall distribution.) Will wrote as if life-expectancy was a median-survival figure, and he 'fessed up when somebody pointed out his mistake, and demonstrated that he does understand what the mistake actually was. Are you as much of a mensch when you screw up?
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