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AP Statistics 1.2 The Language of Variation: Variables- MCQs - Exam Style Questions

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Question

Three brands of candy pieces—X, Y, and Z—are made in many colors. Shaela bought one bag of each brand and counted the number of pieces of each color. The graph below shows the relative frequency distribution of the colors for each bag.
Which of the following statements must be true?
(A) For Brand X, there were more green candy pieces than red candy pieces in the bag.
(B) For Brand Y, there were more red candy pieces than green candy pieces in the bag.
(C) There were more green candy pieces in the Brand X bag than were in the Brand Z bag.
(D) There were the same number of blue candy pieces in the Brand X bag as were in the Brand Y bag.
(E) The number of blue candy pieces in the Brand Z bag was equal to the sum of the number of blue candy pieces in the other two bags.
▶️ Answer/Explanation
Detailed solution

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)

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