Misuse of Statistics
Although statistics can be used as a valuable tool to study many different aspects of the world we live in, be careful.
Many individuals, businesses, and advertising firms misuse statistics to their own advantage.
When examining statistical information, consider the following: • Was the sample used to gather the statistical data unbiased and of sufficient size? • Is the statistical statement ambiguous, could it be interpreted in more than one way?
Example: Misleading Statistics: Describe the misuse of statistics in the following.
1. An advertisement says, “Fly Speedway Airlines and Save 20%”.
2. A help wanted ad read,” Salesperson wanted for Ryan’s Furniture Store. Average Salary: $32,000.”
3. Find the average (mean) of the following numbers: 52, 58, 42, 50, 46, 100, 40, 48, 94, 90 If these numbers were test scores, does the average describe the typical score? Explain.
Graphs can also be misleading, consider the following situation:
We never really know what goes on behind closed doors regarding trades in professional sports.
One (fairly unreliable) source reported that there were secret trade talks that took place between the Boston Celtics and the Los Angeles Lakers after the 2009-10 basketball season. The value of Celtics' guard, Paul Pierce was the topic at hand.
Los Angeles Lakers General Manager: (Excerpt from the report sent to the Boston Celtics. )
“Paul Pierce is not worth much in a trade. His numbers are decreasing quickly and he will soon not be worth any salary.”
Boston Celtics General Manager: (Excerpt from the report sent to the Los Angeles Lakers.)
“Paul Pierce has consistently been one of the top players in the league and his numbers show that he will continue to be a big money player.”
Both graphs of Paul Pierce's stats (from the previous two slides) were based on exactly the same numbers. Neither of the General Managers lied about the stats and both graphs were completely accurate.
The difference between the two graphs is simply the scales used. The Lakers used a scale of 2 on the y-axis (average points per game) and put the data on a broken graph starting with 18 points and going up to 28 points (a range of 10 points) The Celtics used a scale of 10 on the y-axis and showed point averages from 0 to 50 points per game (a range of 50 points).
Compare the data from 2007-08 to the data from 2008-09 in the two graphs above. Which graph seems to display this data correctly? Explain.
Charts and Graphs
Charts and graphs can also be misleading. • Even though the data is displayed correctly, adjusting the vertical scale of a graph can give a different impression. • A circle graph can be misleading if the sum of the parts of the graphs does not add up to 100%.
Here’s another example of misleading graphs:
While each graph presents identical information, the vertical scales have been altered.
Which graph makes Stock A look better? Explain.
In general, individuals, businesses, and advertising agencies will misuse statistics to make themselves, their products, or their clients appear to be better than others.
For a graph to show data to look like there has been significant change:
Use a scale and a range.
** Remember to make data look like there is significant change, a broken graph is often used.
For a graph to show data to look like there has been very little change “flat graph”:
Use a scale and a range.
Example: The following chart shows the percent of the U.S. population that was age 65 and over for the years 1970, 1980, 1990, 2000, and 2010, where the column labeled year refers to the number of years since 1970.
A. Create a graph that would make it look B. Create a graph that would make it look like the population of elderly U.S. residents like the population of elderly U.S. residents has remained stable over the past 40 years. has shown significant increase in the past 40 years.