Question

browntown middle schools principal asks students the language they plan to study in high school. complete the two - way table. describe any association between grade and the language students plan to study.

	grade 6	grade 7	grade 8	total
german		20		57
french	24			54
total	54	70	93	217

Explanation:

Step1: Calculate row - totals

To analyze the association, we first find the row - totals for each language. For Spanish, the total is 101 (46 + 35+ 20). For German, the total is 57 (17 + 20+ 20). For French, the total is 54 (13 + 17+ 24).

Step2: Calculate column - totals

Next, we find the column - totals for each grade. For Grade 6, the total is 54 (18 + 20+ 16). For Grade 7, the total is 72 (35 + 20+ 17). For Grade 8, the total is 73 (46 + 17+ 10). The grand total of all students is 212.

Step3: Analyze the association

We can see that a higher number of Grade 8 students (46) plan to study Spanish compared to other grades for Spanish. Also, the number of students planning to study German is relatively evenly distributed among the grades. For French, Grade 6 has 24 students planning to study it, which is the highest among the grades for French. Overall, there seems to be an association where different grades have different preferences for languages. For example, Grade 8 has a stronger preference for Spanish, while Grade 6 has a relatively high preference for French.

Answer:

There is an association between grade and the language students plan to study. Grade 8 has a higher number of students planning to study Spanish, Grade 6 has a relatively high number of students planning to study French, and the distribution for German is more even among the grades.