Manipulating Statistics Practice Exercises
Review the lesson for Manipulating Statistics Study Guide.
Manipulating Statistics Practice Exercises
List two things wrong with the following survey:
The head of a stock exchange company sent a questionnaire to the firm's employees. It began with an introduction, in which he praised the work everyone was doing to help the company grow, then asked, "Do you believe the federal government has the right to set limits on the bonuses given to hard-working stock brokers in America?"
The survey population isn't random because it only went to people in the firm. Both the introductory material and question show bias—complimenting employees for being hard workers, then using the word "hard-working" to stress that those answering the question would be the ones affected by any government action.
Which is an appropriate conclusion to draw from the following correlation study?
Researchers wanted to know if children's TV viewing affected reading habits. They conducted a study which showed that over 33% of homes with children between the ages of one and six had a TV on most or all of the time. Children in these "heavy-television households" watched TV more and read less than other children do.
- If you own a TV, your six-year-old child will not want to read.
- Children in homes with no TV are better readers.
- Watching TV most of the time may cause one in three young children to read less.
- Children who watch only educational programs read more than children who watch other kinds of shows.
Choice c is the only conclusion that can be drawn from the study. There was no information about educational programs (choice d) or no-TV homes (choice b), and we don't know if your TV is on most or all the time (choice a).
Evidence shows that more car accidents occur on days with clear weather than on days when it is snowing. Can you conclude that it is safer to drive when it is snowing? Why, or why not?
No, other factors influence this statistic, such as the fact that more people are probably on the road in clear weather than snowy weather.
- Is the statistic misrepresented? Ask yourself: is the statistic given in such a way that it misrepresents the data collected—does it make the data sound better or worse than it really is? Suppose a survey is run to find out how many children live below the poverty line. The results are reported on the news: "80% of all children live above the poverty line." So, what about the 20% who live below it? The 80% sounds good, but shifts the focus away from the millions of children who are poor.
Researchers found that 98% of juvenile offenders committing serious crimes watch violent TV shows on a regular basis. If you are an advocate for a reduction in TV violence, how would you use this statistic? What if you were an advocate for freedom of expression on television?
As an advocate for a reduction in TV violence, you would probably say, "Watching violence on TV turns our young people into criminals." If you were an advocate for freedom of expression on television, you might find out the real number of young people in the 2%. Let's say it is 3 million. You might conclude that "millions of children watch violent programs regularly, and they don't end up as criminals."
- Are all the facts there? Another common way to manipulate statistics is to leave out key information. Let's say a bicycle company claims it's edging out its competitor with higher sales. It did have a 50% increase in sales, compared with only a 25% increase for the competitor, but is that "edging out" claim valid? You need more information to know. Suppose the competitor sold 2,000 bikes last year and 2,400 this year; the other company sold 40 bikes last year and 60 this year. Edging out the competition? Hardly!
When you hear a statistic in an advertisement, a political speech, a newspaper article, or other source, remember that it is not necessarily true. Then, ask yourself three questions: Is the statistic meaningful? Does it deliberately misrepresent the data collected? Does it give you all the information you need to evaluate it? Thinking critically about statistics will help you to avoid making the wrong conclusions, or relying on information that is faulty or simply untrue.
What's wrong with this statement?
The teachers in our school system are better off now; they earn an average of $25,000 a year.
We don't have enough information—these teachers are better off compared with what? The salaries of teachers in other school systems in the state? In the nation? What's the cost of living in the area? The teachers could be worse off if $25,000 is not worth what it was last year or five years ago. We also don't know if teachers' salaries cover just a standard 180-day school year or if they have to do after-school and summer programs, or if their total earnings come from teaching alone or if they "earn" at other jobs to supplement their teaching income.
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