September 13, 1990

How to Lie With Statistics

There are three kinds of lies: lies, damn lies and statistics.


To keep us informed, the TV news gave the average incomes of people in the various countries in the Middle East. The conclusion was that the average income in Kuwait was much more than the average income in the rest of the Arab countries.

What does this mean? It means absolutely nothing! Let me explain:

There was a mythical country with a population of 10,000 people. The average annual per capita income was $30,000. Sounds pretty good, doesn't it? The only problem was that 9,999 people had an income of $1,000, while the ruler had an income of $290,001,000.

Aha! a statistics buff says, you should have used the MEDIAN and you would have found that the median was indeed $1,000; the middling income of the people. (To find the median, you make a list, by income level, of all the people in the country. The income of the person in the middle of the list is the Median income.)Is that true? Would the median tell the story?

For that particular country, sort of. But I have another mythical country of 10,000 people where the median income is $30,000. It is distributed as follows:


10 people have an income of $100,000,000

30 people have an income of $1,000,000

40 people have an income of $150,000

5,020 people have an income of $30,000

4,900 people have an income of less than $1000

This country has 49% of the population making less than $1,000 a year, but it has a median per capita income of $30,000.

So, when you hear about the average income in any country, take it with a lot of salt.

What good are statistics then? Actually, there's nothing wrong with statistics. If I showed you a chart like the one above, showing the distribution of incomes, you would have a pretty fair picture of what people earned in a country. A similar graph for height and weights would give you a reliable description of the stature and heft of the people of a country. However, the best description of the significance of averages, means and medians is in Macbeth: "It is a tale told by an idiot, full of sound and fury, signifying nothing."

The title of this article, "How to Lie With Statistics" was the title of a 1954 book by Darrell Huff. It showed how statistics are perverted for profit. It's worth reading. What follows is not from that book; I just borrowed the title.

A TV ad tells you that nine out of ten doctors prefer Bayer. Would the networks allow these people to lie to you? They probably gave 10 doctors large bottles of Bayer aspirin. Nine accepted the gift, and the tenth turned it down. What the commercial neglected to tell you is that Bayer aspirin is no better than the cheapest aspirin that you buy at Pay Less.

A TV ad says that someone ate oat bran and their cholesterol went down 10 points (whatever a point is!). They didn't tell you that if you didn't eat oat bran, that your cholesterol level would also have a 50:50 chance of dropping 10 milligrams per 100ml of blood. If you didn't eat anything, it might really go down. For that matter, if you send the same sample to several different laboratories, the results from one lab to another would vary by considerably more than ten.

The commercial is pure baloney -as are almost all commercials. I said "almost" because I am sure that sleeping on a Serta mattress is better than sleeping on the ground, and eating those vitamin and sugar-packed cereals is certainly better than starving.

Conclusion: If your sixth grade kid doesn't say baloney, or some more pithy expletive, when viewing a commercial, something has been lacking in his education. If your high school age student doesn't at least think it, he may be ruined for life and will only be fit to be a consumer --and an undiscriminating one at that.

The healthiest thing that kids are exposed to nowadays is Mad magazine. It should be required reading. No, I take that back; if it was required, no one would read it.

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