Ask Professor Puzzler
Do you have a question you would like to ask Professor Puzzler? Click here to ask your question!
First of all, I want to make it abundantly clear that this post is not political in nature. It is not an attempt to endorse one candidate, or repudiate another candidate. It is, pure and simple, pointing out how easy it is to misuse mathematics and statistics to try to emphasize a point. Take a look at this image, which is floating around on facebook.
What is the intent of this picture? Well, looking at the caption under the photo, which read, "Who speaks for you? Bernie Sanders 2016," makes it clear that the intent was to show Sanders as a "man of the people" and the rest of them so insanely rich that they are out of touch with the American people.
But the reality is distorted by the image's choice of mathematical language. Specifically, the choice was made to use the text "¾ million" when referring to Cruz's home, instead of the text "750 Thousand." This, I am certain, was deliberate. Because "milllion" sounds massive compared to "thousand," and if they had written "750 Thousand" next to Cruz, people would be much more likely to realize that Cruz is in the same ballpark with Sanders, and not in the same ballpark as Trump, or even Clinton.
To those who are reading quickly, or who didn't do well in math, "¾ million" sounds much larger than "750 thousand," even though the two phrases are expressing exactly the same value.
In mathematical terms, instead of talking about "ballparks" we talk about "orders of magnitude." Two numbers have the same order of magnitude if the larger one divided by the small one is less than 10.
And guess what! Cruz and Sanders have the same order of magnitude. Would you like to see a graph of these values? Here it is:
Notice that compared to Trump, Clinton's homes seem inexpensive, but compared to both of them, Cruz and Sanders are downright indistinguishable*.
Do I care how rich these guys are? Not even a whit. I have no problem with a rich president. I have no problem with a middle class president. I have no problem with a poor president.
I have a problem with people using mathematics to deceive the people who do care about such things. A good piece of advice for you when looking at a set of statistics: take note of all the units given (in this case, "millions" was given as the units throughout, until the very end) and if the units are not consistent throughout, ask yourself why. It may be that there's a good reason, but it could very well be (as in this case) that someone is trying to fool you. To keep things consistent, the graphic creator should either have written the Cruz value as "750 Thousand" or the Sanders value as "3/10 Million."
The person responsible for the graphic probably was hoping for one of the following:
- You slept through the math lessons where your teacher taught you about place value and magnitude.
- You'll be in such a hurry to click "like" that you won't take a moment to remember the lessons you learned.
After all, it's an election year. What did you expect?
* You might be thinking to yourself, "You really think that the difference between a 300 thousand dollar home and a 750 thousand dollar home is not significant?" And if that's what you're thinking, you're sort of missing the point here. The point is that the person who made the graphic was afraid that if he represented the facts in an honest manner, you would think it was an insignificant difference, and so he chose a dishonest path, hoping that your gullibility would do the rest.