How Do You Tell?

We all know that statistics can be in a positive or negative way and we've seen when they are not being properly used. Unfortunately, we can't always tell at a glance that the numbers presented are right. 

Often we hear when statistics are not being used properly, when two graphs are shown with different scales to convince us one product is better than another or one company is better than another. 

Yet there are other numbers out there that are used properly.  How do you help students understand which stats found in life are good and which can be ignored.  Part of teaching mathematics is to help them build a mathematical sense.  A sense of which things such as stats are reasonable and which are not.

If the statistics are used to promote something such as a solution to a problem or a course to help people, chances are the numbers provided may not be fully accurate because advertisers do not meet the same standards that a researcher does.  This means the "Three out of four dentists" recommend the protective power of this particular toothpaste might be suspect because the company wants you to buy it.

Second, if a statistic is used, can it be verified.  Where can I find the "Three out of four dentists" research showing this.  Any statistic that is worth anything can be verified because you should be able to find the study it is based on.  If I hear that some basketball player is able to shoot 4 out of 7 free throws, I should be able to go find that stat in a reputable site such as put out by the NBA.

Third, if the statistic does not seem to line up with reality, question it.  For instance, when I hear that three out of four marriages dissolve in divorce and out of everyone I know most have not divorced but there are a couple who may be on their third, fourth, or fifth marriage, I'd question it.  The multiple divorced people might change the statistic so it seems as if there are more than actually occur.

On the other hand, most sports teams tend to provide verifiable statistics on all players because these stats provide the owners with the necessary information for them to keep, trade, or release players.  Other groups tend to be insurance companies, actuarial companies, census bureaus, and other companies who use the finished data for setting rates.

Insurance companies have had a lot of data to come to the conclusion that females who reach 21 should pay less than their male counterparts since this is a standard practice across the board.  On the other hand, when I read the number of children killed has doubled every year since 1950, I can question that because its easily disproved by simple mathematical equations.

We need to help our students learn to distinguish good stats from bad stats and help them learn to tell the difference.  Let me know what you think, I'd love to hear.  Have a great day.