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Statistics... You're doing it wrong

Updated: May 10, 2023

Speaking for myself, it’s the application of so called “statistical proof” offered in support of a point of view that sometimes drives me up a wall and I’m sure I’m not alone in this regard. Indeed, Mark Twain once said that there are three kinds of lies: lies, damn lies and statistics. On the other hand, according to H.G. Wells “statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write.”

I happen to agree with both of these statements. My purpose here is to sound the alert that the blind acceptance of any politician or special interest group's proffering of statistical facts for or against some issue is dangerous. I want to do so via a couple of demonstrations of how some seemingly obvious fact supported by statistical proof is absolutely wrong. For example, what is the average miles per gallon for two cars, one, an economy car that gets 30 miles per gallon (MPG) and an SUV that gets 10 miles per gallon? Well 10 MPG plus 30 MPG equals 40 MPG and 40 MPG divided by 2 equals 20 MPG. So, the average of these two vehicles is 20 miles per gallon—right?       WRONG Let's, assume both cars travel 1,000 miles. The economy car will use 33.33 gallons of gas and the SUV will use 100 gallons of gas. The total gas consumed is 133.33 gallons and the total distance traveled is 2,000 miles. But 2,000 miles divided by 133.33 gallons of gas is 15 miles per gallon. The true average mileage for these two vehicles is 15 miles per gallon and is known as the “harmonic average.” What about the so called “war on women?” Following is a hypothetical example of six companies and their recent history on giving pay grade promotions to men and women.

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