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Domain Statistics and Probability
Grade 8
Cluster Investigate patterns of association in bivariate data.
Standard Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. <span class='clarification'>For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?</span>
Task Music and Sports

Music and Sports


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Alignments to Content Standards: 8.SP.A.4
Student View

Task

Is there an association between whether a student plays a sport and whether he or she plays a musical instrument? To investigate these questions, each student in your class should answer the following two questions:

  1. Do you play a sport? (yes or no)
  2. Do you play a musical instrument? (yes or no)

Record the answers in the table below.

Student Sport? Musical Instrument?
1    
2    
3    
4    
5    
6    
7    
8    
9    
10    
11    
12    
13    
14    
15    
16    
17    
18    
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24    
  1. Summarize the data into a clearly labeled table.
  2. Of those students who play a sport, what proportion play a musical instrument?
  3. Of those students who do not play a sport, what proportion play a musical instrument?
  4. Based on the class data, do you think there is an association between playing a sport and playing an instrument?
  5. Create a graph that would help visualize the association, if any, between playing a sport and playing a musical instrument.

IM Commentary

  • Vocal training may be considered “playing a musical instrument.”
  • The most commonly used graph to display the relationship between two categorical variables is a segmented bar graph. For segmented bar graphs, we have the categories of the explanatory variable along the $x$-axis (i.e. horizontal axis), with a bar worth 100% at each category. Each bar is split into segments representing the categories of the response variable. The size of each segment is proportional to the conditional proportions of the categories of the response variable, within each category of the explanatory variable.

Solution

Solutions will vary depending on the actual data values collected by the class. Below is a solution based on the following hypothetical data set:

Student Sport? Musical Instrument?
1 Yes No
2 Yes No
3 Yes No
4 No No
5 No Yes
6 Yes Yes
7 No Yes
8 Yes No
9 No Yes
10 Yes Yes
11 Yes No
12 Yes Yes
13 Yes No
14 No No
15 No Yes
16 Yes Yes
17 Yes No
18 Yes No
19 No Yes
20 Yes Yes
21 Yes Yes
22 No Yes
23 No No
24 No Yes

  1. The data can be summarized into a two-way table:

    Sports?
    Yes No Total
    Musical Instrument? Yes 6 7 13
    No 8 3 11
    Total 14 10 24
  2. Of those students who play a sport, the proportion who play a musical instrument = $\frac{6}{14} = 0.43$
  3. Of those students who do not play a sport, the proportion who play a musical instrument = $\frac{7}{10} = 0.70$
  4. Based on the above data, it appears that students who don’t play a sport, are more likely to play a musical instrument compared to students who do play a sport, as can be seen from the answers to (b) and (c). 

  5. Here is a segmented bar chart for the above data:

    Sol_1_f40c2939c2a0aaa0354ce0dbb07f3c34

    As can be seen from the above graph, of all those students who reported not playing a sport, 70% reported playing a musical instrument, whereas 30% reported not playing a musical instrument. On the other hand, of all those students who reported playing a sport, about 43% reported playing a musical instrument, compared to 57% reported not playing a musical instrument.

Music and Sports

Is there an association between whether a student plays a sport and whether he or she plays a musical instrument? To investigate these questions, each student in your class should answer the following two questions:

  1. Do you play a sport? (yes or no)
  2. Do you play a musical instrument? (yes or no)

Record the answers in the table below.

Student Sport? Musical Instrument?
1    
2    
3    
4    
5    
6    
7    
8    
9    
10    
11    
12    
13    
14    
15    
16    
17    
18    
19    
20    
21    
22    
23    
24    
  1. Summarize the data into a clearly labeled table.
  2. Of those students who play a sport, what proportion play a musical instrument?
  3. Of those students who do not play a sport, what proportion play a musical instrument?
  4. Based on the class data, do you think there is an association between playing a sport and playing an instrument?
  5. Create a graph that would help visualize the association, if any, between playing a sport and playing a musical instrument.
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