Yesterday, WITF reported the following:
Pennsylvania is home to 120,000 high school dropouts between the ages of 16 and 24. Now, the Pennsylvania Partnerships for Children is launching an effort to re-connect those young people by helping them get their GED and pursue post secondary education or an associates degree. President and CEO Joan Benso says high school dropouts are a drain on the economy because they are more likely to be unemployed, get arrested and live in poverty. "Every high school dropout under the age of 25 costs the taxpayers at least $683 a year more in state and federal and local supported services than they consume." she says. Benso says nearly 50 percent of the jobs in Pennsylvania require more than a high school diploma, but less than a bachelor's degree -- so, that's an area her group is hoping to move dropouts into. She hopes the next governor will make dropout re-engagement a priority.
Now, this is a pressing concern, and I don't mean to minimize it. But, it does bring up an important mathematical distinction that has been misused here. It is the difference between "every" and "average". Look at the quote by Ms. Benso above, and I will explain what I mean.
First, average can be used for several different measurements. In this case, the average being used is the mean, what most people think of as the average. It is where you add up all the values in a set and then divide by the number of values you had. I looked up the statistic Ms. Benso was quoting, and the number $683 is the mean of the amount that high school dropouts are consuming in services minus the amount they are contribuing in tax dollars.
So what's the difference, right? What Ms. Benso could accurately say is "The average high school dropout under the age of 25 costs the taxpayers..." rather than "Every high school dropout..." Saying every means that if you pick any single high school dropout in PA under the age of 25, that person costs the taxpayers $683 more for services than they give back in tax dollars. Every single one is exactly the same, and is costing taxpayers money.
But what's really true is that some high school dropouts in PA under the age of 25 cost the taxpayer a lot more than $683, and others cost less. Some might even be contributing more in taxes than they are consuming. Yes, on average, each dropout costs us money. But any individual dropout could be doing very well in terms of income and taxes paid in.
Is it important? In this instance, perhaps not. But take a different example. The average American costs $1066 in health care expenses annually. If this were "every American costs $1066 in healt care expenses annually", that means would have to charge at least $1066 in annual premiums, really much more to make a profit. Because they would be paying out this amount for everyone they covered. The people who are just going to the doctor for physicals are only spending a couple hundred dollars. But some people with massive medical needs are spending hundreds of thousands of dollars. If you are young and healthy, you don't want your insurance premiums to be based on everyone, you want it to be based only on people like you, young and healthy. So you want the insurance companies to recognize an average as an average, not as an every.
So, when you are stating numerical facts, always be careful about the word "every." Every may seem very similar to average, but on average, they are nothing alike.
