Statistics is one of the most useful applications for math, but statistics often gets a “bad rap”. This is mostly due to misunderstandings about methods and uncertainty (errors).
Statistical Methods: Average or Mean
Most people know how to compute averages. Averages are very useful, but if applied incorrectly, averages can be very misleading. Here is an example:
Example 1
Room A has 10 people who, together, have an average income of $50,000.
Room B has 10 people who have an average income of $1,000,000.
Question: Are the people in room B better off financially than those in Room A?
Answer: Maybe not.
For room A, suppose 5 people make $60,000 each, and 5 people make $40,000.
Total wages = $500,000. $500,000/10= $50,000 average.
For room B, 9 people make $8,000 each, and 1 person makes $ 9,928,000.
Total wages = $10,000,000. Average is $1,000,000.
This is an “extreme” example of how averages may be not be the best statistic. Most of the people in room B would be considered poor when compared with those in room A!
Uncertainty
In politics, many polls are taken to try to predict a winner. The news reports on these polls often do not tell you the “margin of error” in the polls, or how the polls are taken.
The margin of error is a measure of uncertainty.