AP Statistics 2.1 Tabular and Graphical Representations for the Distributions of Two Categorical Variables- Exam Style Questions - MCQs - New Syllabus
▶️ Answer/Explanation
The bar chart shows percentages, but the sample sizes are different:
\(n_{\text{Rockland}}=300\)
\(n_{\text{South Lake}}=200\)
For students whose college choice is more than 100 miles away:
Rockland: approximately \(2\%\)
\(0.02(300)=6\text{ students}\)
South Lake: approximately \(10\%\)
\(0.10(200)=20\text{ students}\)
So (E) is false.
For students choosing a college within 10 miles:
Rockland: approximately \(30\%\)
\(0.30(300)=90\text{ students}\)
South Lake: approximately \(40\%\)
\(0.40(200)=80\text{ students}\)
So (C) is false.
For students choosing a college 50–100 miles away:
Rockland: approximately \(28\%\)
\(0.28(300)=84\text{ students}\)
South Lake: approximately \(15\%\)
\(0.15(200)=30\text{ students}\)
Since:
\(84 > 2(30)=60\)
more than twice as many students at Rockland chose colleges 50–100 miles away compared with South Lake.
Therefore, the statement supported by the graph is choice (D).
✅ Answer: (D)
▶️ Answer/Explanation
The question asks for the proportion of homes that are either ranch or cottage.
From the totals row:
\(\text{Ranch} = 50\)
\(\text{Cottage} = 24\)
Since a home cannot be both a ranch and a cottage, add the counts:
\(50+24=74\)
The total number of homes sampled is 132, so the required proportion is:
\(\frac{74}{132}\)
Therefore, the correct answer is choice (D).
✅ Answer: (D)
▶️ Answer/Explanation
To check statement (D), calculate the percentage of Grade 11 students who selected blue:
\(\frac{7}{26}\times 100 \approx 26.92\%\)
This rounds to approximately 27%, so statement (D) is supported by the data. The other options are not supported because yellow is not the least chosen color overall, Grade 10 does not have the largest total, the percentage choosing red is about \(\frac{31}{110}\times100\approx28\%\), and blue was not the least chosen color in Grade 9.
✅ Answer: (D)