Activity to Show Sample Population and Bias
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Backpack Colors Investigation

Students will utilize pre-existing data pertaining to the color of backpacks used by high school freshmen for a statistical study.   In the process of this investigation, students will examine sample populations and bias.

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for use in your classroom.

The data appearing in the following charts was obtained from LHS High School using 582 students from the Freshman class who carried backpacks.  The data pertains to the color of backpacks the students carry to school.  Groups of students conducted surveys to obtain the data charts that appear below.

Chart 1:  Data collected from the entire population
                    (collected by surveying Freshmen carrying backpacks  -  582 students)

Backpack color black brown blue red yellow purple pink other
Response from boys (292) 91 58 66 32 14 9 2 20
Response from girls (290) 40 15 72 55 20 31 32 25
Totals 131 73 138 87 34 40 34 45


Chart 2:  Data collected from a random sample population
                    (collected by surveying Freshmen carrying backpacks and attending period two Study Hall - 54 students)

Backpack color black brown blue red yellow purple pink other
Response from boys (32) 12 2 10 6 0 1 0 1
Response from girls (22) 2 0 8 6 2 2 2 0
Totals 14 2 18 14 2 3 2 1

 

Chart 3:  Data collected from a biased sample population
                    (collected by surveying Freshmen girls carrying backpacks and attending period 8 gym class - 42 students)

Backpack color black brown blue red yellow purple pink other
Response from girls (42) 7 0 8 12 4 4 6 1

 

Chart 4:  Data collected from a biased sample population
                    (collected by surveying Freshmen boys carrying backpacks and attending period 3 gym class - 36 students)

Backpack color black brown blue red yellow purple pink other
Response from boys (36) 16 2 8 7 1 2 0 0

 

Students will be asked to prepare bar graphs to visualize the data.

Armed with the charts and graphs, students will discuss the statistical implications of this study.
 

Questions for discussion/response:

1.  Are the results from the entire population what you would have expected them to be?

2.  What factors might influence a student's choice of color for a backpack?

3.  Why do you think that blue was the most popular color for the entire population?

4.  How similar is the data collected from the random sample population with the entire population?  Compare and contrast.

5.  Would the random sample population data in this study be a good predictor for the entire population?  Explain.

6.  Examine the results from the biased sample populations.  Why are these charts labeled as "biased"?

7.  What are the similarities and differences between the two sets of biased data?

8.  Would either of the biased sample population data in this study be good predictors for the entire population?  Explain for both sets of biased data.

9.  If the two biased sample sets were combined, would they produce sample data that would be a good predictor for the entire population?

10.  If the three sample populations were combined, to form a larger sample population, would the result be a good predictor for the entire population?