Exact is Not Accurate

Numbers.

Over the next few years, you’ll be certain to see a barrage of numbers thrown at you.  While researching the latest atrocity promoted by the administration, I came across the following tidbit:  The average tuition for private schools is $10,003.

Now, if I want to include this in a blog, vlog, Facebook post, or public speech, I have a conundrum.  Compare the two sentences:

  • The average tuition for private schools is $10,003.
  • The average tuition for private schools is about ten thousand dollars.

The first sounds like I know what I’m talking about:  that I’ve done some high-level research and wrestled a number to the ground.  The second sounds like I spent thirty seconds on  Google.  (Actually, the first number was based on thirty seconds on Google)

The difference is that I sound more convincing with the exact figure.  In fact, there’s a story (which might  or might not be true) that when the first surveyors found the height of Mount Everest, they came to a value of 29,000 feet…but they published it as 29,002, because that sounded more accurate.

The problem is the exact figure might not be accurate.  Consider the two statements:

  • The population of the United States is 324,595,182.
  • The population of the United States is 325 million.

The first gives an exact number, and sounds very accurate.  But it is almost certainly false.  In particular, even if the population of the US was 324,595,182 at some point, it is almost certainly not 324,595,182 right now.  On the other hand, it’s still about 325 million, and will be so for awhile.  (I talk about this in my FOCUS article).

There’s a concept in the sciences called significant figures.  The gist of it is this:  When I give you a number, I am giving you a guarantee that the non-zero digits of the number are correct.  (The zeroes are a little more complicated:  if you want a crash course on signficant figures, here’s the video I have my students watch)

  • If I claim 324,595,182, then I’m guaranteeing each and every digit is exact…and if the population is 324,595,183, then I’ve fed you misinformation.
  • If I claim 324 million, then I’m guaranteeing that the population is somewhere between 323,500,000 and 324,499,999 (since anything in this range would round to 324 million).

What’s the big deal?  One problem with statistics is that people don’t believe them.  You’ve heard the quote:  “There are three types of lies:  Lies, damned lies, and statistics.” I suspect part of the reason is that if someone says “The average tuition at private schools is $10,003,” they can respond with “But at our school, it’s $7500, so how do you get an average of $10,003?”   This generally leads to a discussion of how to calculate averages, and often degenerates into accusations of skewed samples.

On the other hand, if you say “The average tuition at private schools is around $10,000,” then to the person who says “But we only pay $7500,” the response is “Which is around $10,000.”  By avoiding the mechanics of computing the number, we focus on the value itself.

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