AP Statistics 1.4 Graphical Representations for One Categorical Variable- Exam Style Questions - MCQs - New Syllabus
▶️ Answer/Explanation
The fastest 25% of runners correspond to the first quartile (Q1), since the first quartile marks the point below which 25% of the observations fall.
On a boxplot, \(Q_1\) is represented by the left edge of the box. Looking at the graph, the left edge of the box is slightly above 16 minutes, approximately:
\( Q_1 \approx 16.25 \text{ minutes} \)
This means that about 25% of the runners completed the race in 16.25 minutes or less.
Therefore, the fastest 25 percent of runners have a typical time of at most approximately 16.25 minutes.
✅ Answer: (B)
▶️ Answer/Explanation
1. Interpret the Graph:
The graph shows relative frequencies (proportions), not actual counts. We can only compare the proportions of colors within the same brand’s bag.
2. Analyze Brand Y:
– The proportion of red pieces for Brand Y is approximately \(0.50\) (from \(0\) to \(0.50\)).
– The proportion of green pieces for Brand Y is approximately \(0.30\) (from \(0.50\) to \(0.80\)).
Since \(0.50 > 0.30\), the proportion of red candy pieces was greater than the proportion of green candy pieces in the Brand Y bag. Because we are comparing proportions within the same bag, this means there were more red pieces than green pieces.
✅ Answer: (B)