This tweet caught my eye a few weeks ago. It was from a well-known political commentator for a major US newspaper, who I follow. I am obscuring his name since his identity is not relevant to this post. What does bother me, is that an influential commentator with a large pulpit can display such a lack of number sense. (I still enjoy reading him; he has a good grasp of many things. But not where numbers are concerned.)
In fact, the tweet did more than catch my eye; it jumped right off the screen and nigh on blinded me. Regardless of whether the initial assumption is correct or not, the conclusion is so obviously wrong on simple numerical grounds.
As usual, a very simple, made-up example is all it takes to highlight the fallacy. Also as usual in such situations, virtually no mathematics is involved here, and no arithmetic beyond very simple stuff with whole numbers. Number sense is not arithmetic. The goal is to get a quick numerical sense of the issue
Assume that a worker making $25,000 a year in 2010 saw their wages rise by 5% over the ten-year period to today. They would now be making $25,000 + $1,250 = $26,250. Compare that with their boss, who made $100,000 a year in 2010 but whose income rose only by 2.5%. In 2020, they bring in $100,000 + $2,500 = $102,500. Their pay increased at half the rate of their low-paid employee, but that meant their income rose by twice as much.
As with the example of the “danger of drinking wine” I wrote about last time, it all depends on the base figures on which the percentages are calculated.
How close to reality is my made-up-on-the-spot, number sense example? I googled “rise in wages”, and immediately found myself looking at a recent report from the Brookings Institute that gave me all I need. (I chose a page from a source I knew to be reliable.) For the low-paid worker, my example was not too far off. From 2010 to 2018, the bottom 10th percentile of hourly wages grew 5.1%. But I was way off with my number for the boss. In fact, the entire top 90th percentile of workers saw their income go up by an average of 7.4%.
What this tells us is that the opinion writer not only has poor number sense, he is not even able to get his underlying numerical facts right. Of course, you might say the writer set out to deliberately mislead. That’s possible, I suppose, but I doubt it. His article was in a major national newspaper that has fact-checkers, so both he and the publisher knew that his claims could easily be checked. To continue doing his job, readers have to trust him. Much more likely, I think, the issue was innumeracy. Like many people I know, when faced with figures, both the writer and his editor likely found their eyes glazing over.
Yet to anyone with number sense, the writer’s tweet jumps off the page as being absurdly wrong. What the actual numbers are does not matter. Even if his assumption about the relative rises had been correct, his conclusion would be false, as my initial made-up example showed.
In fact, my one use of google showed that even his starting point was off-the-charts, factually wrong: wages of higher-paid workers had risen a lot faster than for those at the bottom.
The sad fact is that the majority of people in the media have very poor educational backgrounds in mathematics, science, or engineering. Numbers are alien to them.
Given the huge significance of numerical data in today’s world, that tells us that our educational system needs to change. Arguing about the pros and cons of teaching Algebra 2 or Calculus seems totally misplaced, when we are producing so many people who lack basic numeracy.
In the meantime, if we cannot rely on the media to get the numbers right—by which I mean, ballpark, number-sense, appreciate-it-when-you-see-it right—then it is up to we citizens to protect ourselves from being misled.
And, for those of us in the education business, to make sure our students can be both good consumers of quantitative information and good communicators of numerical data.
Mathematics Outreach Project (SUMOP) 