Man drowns in a river with an average depth of one (1) inch
With all of the polls and statistics bandied about this election year, it made me think again of the high levels of innumeracy present in our society. I wish to reiterate the harmful social effects of innumeracy, given that most examples in use today have you consider trade-offs between two conflicting outcomes (e.g., Bush v. Kerry), outcomes that will change your life.
- Bush at 48%, Kerry at 47%, with a ±5% margin of error. So who is ahead?!? Either, both, none!?! Depends on the spin.
A silly example, that is my favorite because it encompasses the most popular application of numbers. That is a percentage based on a very small or biased sample of respondents.
- 80% of dentists recommend chewing Dentine, Smith could not be persuaded.
In an increasingly complex world filled with data and information, what is needed most is not more or better data, statistics, and information, but a better command of existing data and information. For this, a good course in statistics and probability is a must. A course covering cause and correlation, independence, the multiplication and additive principles, expected returns and probability distributions. I don't mean to say another course with algorithms and such, but a practical one that explains the everyday occurrences of numbers, statistics and probability.
Probability and statistics is not just for mathematicians. It infuses our lives every day. Innumeracy is the inability to comfortably deal with the fundamental notions of numbers, statistics and chance. It is a national plague. Who is an innumerate? Here are two examples:
- These are the people who hear there is a 50% chance of rain on Saturday and a 50% chance of rain on Sunday, concluding that there is a 100% chance of rain for the weekend, or
- The state legislator in Wisconsin who objected to the introduction of daylight savings time despite all the good arguments for it. He maintained sagely that there is always a trade-off involved in the adoption of any policy, and that if daylight savings time were instituted, curtains and other fabrics would fade more quickly. This poor fellow thought that the days would be longer, i.e., 25 hours.
The problem permeates every aspect of our lives, and begins with the basics of understanding numbers: Small versus very large numbers. I once asked a friend to estimate the speed a snail moves in miles per hour. He responded, they can't travel that fast, and hence the number could not be estimated. He had an MBA from an Ivy league school! The correct answer may be 0.005 miles per hour!
Another problem is understanding scale. With regards to Noah's Ark, it was said " ... all the high hills that were under the whole heaven were covered ..." This seems to indicate that there was 10,000 to 20,000 feet of water on the surface of the earth, that is almost half a billion cubic miles of water. And so if it rained for 40 days and 40 nights, or 960 hours (1000 hours in Wisconsin), the rain must have fallen at an average of 15 feet per hour. That must have been some Ark that Noah engineered. Where did all that water come from? Where did it go?
Small numbers versus large numbers, and the whole concept of scale are just the tip of the innumeracy iceberg. I don't wish to make this a math tutorial, but to speak to the need for an education system, that helps us better prepared to understand numbers and statistics that are thrown our way. So that we can question things, and to understand the responses. The major problem is that most teachers themselves are innumerate. So let us start with them.
Contributed to Boroumand by A.R., San Rafael, California, 2004
Take Away Lessons For the Guilty
It is critical that one becomes numerate. This begins at our schools and at the lowest levels. To make people numerate is the responsibility of ever teacher not just math teachers.
Teachers and the innumerate, purchase and read Statistics For Dummies, or any and all other books that can help you.
Teach your children early. Teach them about numbers and chance.
Don't ever tell your girls that math is for boys.