How to Lie With Statistics: Chapter 2: The Well-Chosen Average

First off, if you haven’t read the first chapter of this book, please go back and read my review of the 1st chapter: The Sample with the Built in Bias. It’s phenomenal, you’ll love it.

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How to Lie With Statistics: Chapter 2: The Well-Chosen Average

The book opens up with a specific example:

“You, I trust, are not a snob, and I certainly am not in the real-estate business. But let’s say you are and I am and that you are looking for property to buy along a road that is not far from the California valley in which I live.

Having sized you up, I take pains to tell you that the average income in this neighborhood is some $15,000 a year. (This book is from 1954) More than likely, since we have agreed that for the purposes of this moment you are a bit of a snob, you toss it in casually when telling your friend about where you live. “ (Pg. 27)

(Now for this book, I suggest adding a 0 to each number. Imagine this income was $150,000 average which would be a great deal of money as an average income in a neighborhood, unless you read further.)

(The author continues to follow this example but he adds a twist when a year later he starts petitions to keep taxes low.)

“My plea is we cannot afford the increase: After all, the average income in the neighbored hood is only $3500 a year. Perhaps you go along with me and my committee in this — you’re not only a snob, you’re stingy too — but you can’t help being surprised to hear about that measly $3,500. Am I lying now, or was I lying last year?” (Pg. 28)

(This is where it starts to get interesting. The author shows us how he used the statistics to not lie, but bend the truth to his favor when he needed to use the $15,000 a year mark as a higher income to entice you. Again, if you need help making this make sense, add a 0 to the income. $35,000 as a yearly income isn’t measly but it’s certainly low.)

(Now the author gives a small paragraph explaining how he used the word “average” to deceive us.)

“That is the essential beauty of doing your lying with statistics. Both of those figures are legitimate averages, legally arrived at. Both represent the same data, the same people, the same incomes. All the same it is obvious that at least one of them (the income figure) must be so misleading as to rival an out-and-out lie.” (pg. 28)

(I love this part, I felt like an idiot when I read this. Personally I’m bad with understanding how averages can differ but words do not elude me. So as a person who loves using twisted phrases or double meanings, this had me waiting for the punch line.)

“The trick was to use a different kind of average each time, the world ‘average’ having a very loose meaning.” (Pg. 28)

(Here we go, he’s going to show us how statistics can be used to trick common people very easily when it comes to the word average.)

“The $15,000 figure I used when I wanted a big one is a mean, the arithmetic average of incomes of all the families in the neighborhood. You get it buy adding up all the incomes and dividing by the number there are. The smaller figure ($3,500) is a median, and so it tells you that half the families in question have more than $3,500 a year and half have less. I might have closed used the mode, which is the most frequently met-with figure in a series.” (pg. 28)

(The author shows us how easily he can trick us the reader by picking whichever number he wants to use at any moment. This is the worst way to use the word average. This method is used by marketers all the time. )

“In this case, as usually true with income figures, an unqualified ‘average’ is virtually meaningless. One factor that add to the confusion is that with some kinds of information all the average fall so close together that, for casual purposes, it may not be vital to distinguish among them.” (pg. 29)

(This is where the author is going to show us a major difference between things in the physical world versus the non-physical world.)

“…different averages come out close together when you deal with data, such as those having to do with many human characteristics, that have the grace to fall close to what is called the normal distribution. If you draw a bell curve to represent it you get something shaped like a bell, and mean, median, and mode fall at the same point.” (pg. 30)

“Consequently one kind of average is good as another for describing the heights of men, but for describing there pocketbooks it is not.” (pg. 30)

(This is what is so interesting overall to me. We have entered a world where we deal less with the physical world and more with the digital or “data” world. Now we enter into places where we have a higher rate of interaction with fat tail data. If you’re not familiar with fat tail data it’s when you get an gigantic effect from a very small percentage. Think of the top 1% of income earners in the world then think how many standard deviations their income is away from the mean. The fact a majority of the world makes less than $10 a day but Bill Gates have over $49 Billion dollars show how the 1% probability has a greater weight than the other 99%.)

(The author uses a similar example as he describes how he arrived at the “average” for your neighborhood.)

“It happens that most of your neighbors are small farmers or wage earners employed in a near-by-villiage or elderly retired people on pensions. But three of the inhabitants are millionaire week-enders and these three boost the total income, and therefore the arithmetic average, enormously. They boost it to a figure that practically everybody in the neighborhood has a good deal less than. You have in reality the case that sounds like a joke or figure of speech: Nearly everybody is below average.” (pg. 31)

This has been a review of How to Lie With Statistics — Chapter 2: The Well-Choosen Average.

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What did you think about this post? Have you ever had a time when you thought someone meant one average verse another? Also, how do you think knowing this can help you not get tricked by a slightly-shady real estate agent?