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Grade 8
Domain Statistics and Probability
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 What's Your Favorite Subject?

What's Your Favorite Subject?


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Alignments to Content Standards: 8.SP.A.4
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Task

All the students at a middle school were asked to identify their favorite academic subject and whether they were in 7th grade or 8th grade. Here are the results:

Favorite Subject by Grade
Grade English History Math/Science Other Totals
7th Grade 38 36 28 14 116
8th Grade 47 45 72 18 182
Totals 85 81 100 32 298

Is there an association between favorite academic subject and grade for students at this school? Support your answer by calculating appropriate relative frequencies using the given data.

IM Commentary

Either row percentages or column percentages are appropriate for the solution, since there is no clear explanatory/response relationship between the variables. Whether the student sees a strong association or not is less important than whether his or her answer uses the data appropriately and understands that an association means that the distribution of favorite subject is different for 7th graders and 8th graders.

Another approach is to observe that 39% of the students are 7th graders. If grade is not associated with favorite subject, you would expect about 39% of the students picking a particular subject as their favorite to be 7th graders.

Solution

Row relative frequencies (that is, distribution of the variable “Favorite Subject” for each grade) are given in the table below.

Favorite Subject by Grade
Grade English History Math/Science Other
7th Grade 0.328 0.310 0.241 0.121
8th Grade 0.258 0.247 0.396 0.099

There is some association between favorite subject and grade. A higher percentage of 7th graders than 8th graders prefer English and History (and - to a lesser extent - “other” subjects), while a higher percentage of 8th graders than 7th graders prefer Math/Science.

What's Your Favorite Subject?

All the students at a middle school were asked to identify their favorite academic subject and whether they were in 7th grade or 8th grade. Here are the results:

Favorite Subject by Grade
Grade English History Math/Science Other Totals
7th Grade 38 36 28 14 116
8th Grade 47 45 72 18 182
Totals 85 81 100 32 298

Is there an association between favorite academic subject and grade for students at this school? Support your answer by calculating appropriate relative frequencies using the given data.

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