6th Grade - Misleading Questions And Graphs

 
     
 
     
 
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6th
Statistics
Misleading Questions and Graphs
Analyze data displays and explain why the way in which the question was asked might have influenced the results obtained and why the way in which the results were displayed might have influenced the conclusions reached.
Study data displays (i.e. graphs, charts, tables, etc…) and the wording of questions used to compile a set of data. Determine if the data results and conclusions have been influenced by the data display or question. Understand that biased questions cause misleading data. Biased questions give a prejudiced view of a topic or influence the sample group to answer in a specific way. Data displays can be misleading when the scale suggests changes or differences that are greater than they really are. Analyze the question and presentation of data to determine if it is misleading in any way. Determine of a data conclusion is biased (misleading or unfairly represents the target population) or representative (fairly represents the target population) based on both the question asked and data display.
 

Sample Problems

(1)

Determine whether the survey question is biased or representative. Explain.

The high school coach asked all the kids in his P.E. classes the following survey question. Is your favorite sport football?

(This question is biased, because the coach is suggesting football as a favorite by naming it.)

(2)

Determine whether the survey question is biased or representative. Explain.

The high school coach asked all the kids in his P.E. classes the following survey question. What is your favorite sport?

(This question is unbiased, because it does not suggest any sport and allows the respondent to answer without any direction.)

(3)

Determine whether the survey question is biased or representative. Explain. Sal wanted to find the most popular ice cream flavor. He asked, “Is chocolate your favorite ice cream flavor or is it vanilla?”

(This question is biased because Sal is suggesting chocolate by stating it first with the word favorite and puts vanilla all the way at the back of the question.)

(4)

Determine whether the data display is biased or representative. Be sure to look closely at the scale.

(This data display is unbiased. The scale uses at regular intervals of 50.)

(5)

Determine whether the data display is biased or representative. Be sure to look closely at the scale.

(This bar graph is misleading because it does not start at zero. It causes the reader to believe that Overachiever has a score almost 3 times greater than Dullsville. However, if you look closely at the scores, Dullsville has 301 points and Overachiever has 305. This nowhere near 3 times greater and in fact, the scores both schools are very close.)

Learning Tips

(1)

Statistics are often reported in an effort to convince people of a point of view. The use of figures such as, tables, graphs and charts are intended to provide support for the point of view being portrayed. It is important to understand that flaws in research or even intentional data presentation can lead to false or unsupported conclusions being drawn. The nature of a survey question and data display can greatly influence conclusions. It is most important to understand that the entire process of gathering and displaying data must be analyzed to ensure a fair representation has been made before drawing any conclusion. There are three main areas where statistics can go wrong: a biased question, a biased sample group, and a misleading data display. Each of these should be evaluated and by the data viewer, before drawing or believing any conclusion or point of view influenced by the data. When evaluating a data conclusion you may want to use the checklist below:

  • Unbiased question

  • Unbiased sample

  • Data display starts and zero and has even intervals

If you can check mark all three areas then it is justified to draw conclusions from the data or consider agreeing with the point of view. However, if even one area is not checked, any conclusions drawn will be misleading.

(2)

It is crucial to understand the type of question asked when the data was gathered. There are two question types: biased questions and unbiased questions. Unbiased questions are fair; they don’t try to influence the person being interviewed in one way or another. Unbiased questions will give good answers that fairly represent the target population. Only surveys using these types of questions should be trusted. An example of an unbiased question is, “What is your favorite sport?”. On the opposite end of the spectrum are biased questions. Children often confuse these new vocabulary terms and may need to use the statement “Biased is bad,” to help them remember. Biased questions can be considered bad because they try to influence the respondent’s answer. An example of a biased question would be, “Is volleyball your favorite sport?”. This question is biased because it is suggesting that volleyball is an answer. Biased questions will always try to lead the respondent to the answer the question writer wants. One way to do this is by suggesting an answer, such as in the question below. A second way to do this is to put pressure on the respondent so that he/she will answer in a particular way. For example, a question can be prefaced with a statement to make a respondent feel pressured to respond in a certain way. Here’s an example: “Teens across America voted Soccer as their favorite sport. What is your favorite sport?” To show the importance of how a question is asked, give your child a topic and have him/her use it to write an unbiased and biased question. Then have him or her use both questions to ask different people one of the questions. Finally, have them compare the results from the people who responded to the biased question vs. those who answered the unbiased question. Be sure the sample group your child uses has some sort of similarity (boys and girls ages 10-12, etc…).

(3)

Another leading cause of unsupported or incorrect conclusions based on data are misleading data displays. Data can be displayed in a variety of ways: line graphs, bar graphs, scatter plots, etc… There are three common errors that cause a misleading graph, which causes incorrect conclusions. The first is a graph with a scale that does not begin with a zero. Next, is a graph scale with uneven intervals with no real pattern (i.e. the scale counts as follows: 0, 1, 2, 4, 6). The third is missing categories (year, months, etc…). All data displays with any of the aforementioned problems will lead to erroneous conclusions.

(4)

All consumers and voters young and old need to take responsibility for learning how to accurately view data and draw their own conclusions. Most often survey questions are designed to influence the consumer. Other times, data displays are used to mislead him/her. You may want to find samples of online surveys and use them to determine which questions are biased and which are not. The same can be done for data displays.

(5)

The vocabulary terms and concepts in this skill don’t become real for many children unless they are given the opportunity to collect the data themselves. You can provide this experience for your child by helping him/her create and conduct a survey of his/her own. However, it will work best if he/she first conducts an unbiased survey and follows up by conducting biased survey with the same topic. He/she should not interview the same people as the first, on the second survey. After both surveys are concluded, you can discuss the difference in the results and the power of bias.

(6)

The visual learner may need to use graph paper to create two graphs showing the same data. He/she would draw the first with the correct scale and the second with either a missing zero or uneven intervals.

Extra Help Problems

(1)

Determine whether the survey question is biased or unbiased (representative). Explain.

Would you rather eat a cheeseburger or the usual cheese sandwich?

(Biased, it shows favoritism to the cheeseburger over the sandwich.)

(2)

Determine whether the survey question is biased or unbiased (representative). Explain.

Is your favorite sport soccer?

(Biased, it is based on an assumption that soccer is even a choice.)

(3)

Determine whether the survey question is biased or unbiased (representative). Explain.

Red is the most popular color at Russell School. Is red your favorite color?

(Biased, this question is suggesting that other colors are unpopular in an attempt to sway the answerer to go along with the rest.)

(4)

Determine whether the survey question is biased or unbiased (representative). Explain.

How many hours a night do you spend completing homework?

(Unbiased, this question allows each person to answer honestly with no influence.)

(5)

Determine whether the survey question is biased or unbiased (representative). Explain.

Teachers recommend that students spend about one hour completing homework each night. How many hours do you spend on homework?

(Biased, the person being surveyed will feel pressured to answer one hour or more.)

(6)

Determine whether the survey question is biased or unbiased (representative). Explain.

Do you believe that school cafeteria food is nutritious?

(Unbiased, this question is not influencing an answer one way or the other.)

(7)

The line graph below shows the total hours spent completing homework for four weeks. On the graph, it looks like the hours spent on homework from week 2 to 4 have only increased slightly. Is this a reasonable conclusion to draw? Explain.

(No, if you look at the numbers, 8 hours of homework were completed in week 2 and 16 hours were completed in week 4. This is double the amount, which is not represented by the line graph. The scale of the line graph causes misleading conclusions to be drawn because it moves up in uneven intervals.)

(8)

Is the data display misleading or representative of the data collected? Explain.

(The bar graph is misleading, because the scale skipped the interval 200.)

(9)

Is the data display misleading or representative of the data collected? Explain.



(The line graph is representative of the data collected because the scale is presented in equal intervals.)

(10)

Looking at the bar graph below, the conclusion could be drawn that house sales have tripled from 1998 to 1999. Is this a valid conclusion? Explain.


(This is an invalid conclusion, because the bar graph is misleading. Since the scale jumps to 80,000 right away, it makes the increase seem larger. There is actually only a 2,000 difference between 1998 and 1999.)


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