AP®StatisticsCollege BoardExam QuestionsUnit 1: Exploring One-Variable DataGraphical Representations

Graphical Representations (College Board AP® Statistics)

Exam Questions

5 mins5 questions
1
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Of the following dotplots, which represents a set of data with a negatively skewed distribution?

  • A dotplot with a horizontal axis labeled 0 to 8. Points are represented by asterisks that decrease in density from left to right along the axis.
  • A dotplot with a horizontal axis labeled 0 to 8. Points are represented by asterisks that increase in density from left to right along the axis.
  • A dotplot with a horizontal axis labeled 0 to 8 and points represented by asterisks. Peaks occur at 2 and 7.
  • A dotplot with a horizontal axis labeled 0 to 8 and points represented by asterisks. The distribution is roughly symmetrical and is centered at 4.
  • A dotplot with a horizontal axis labeled 0 to 8 and points represented by asterisks. All values have two points except for 0 and 4, each of which has one point.

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2
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Which of the following histograms could have been constructed from the same set of data summarized by the boxplot below?

Boxplot plotted along an axis from 0 to 100. The vertical line at the end of the left-hand whisker is at 17, the first vertical line of the box is at 63, the vertical line inside the box is at 78, the last vertical line of the box is at 89, and the vertical line at the end of the right-hand whisker is at 98.
  • A histogram with the x-axis labeled from 0 to 100 in intervals of 10 and the y-axis labeled "Frequency" from 0 to 30 in intervals of 10. The data has a symmetrical "bell" shape and is centered around 50 to 55.
  • A histogram displaying the data frequency distribution from 0 to 100 on the x-axis, peaking between 70 and 80, with a tail towards the lower end of the x-axis. Frequency on the y-axis ranges from 0 to 30.
  • A histogram displaying the frequency distribution of data values ranging from 0 to 100 in intervals of 10, with frequency values on the y-axis up to 30. Values throughout range from 6 to 14.
  • A histogram with two peaks on the x-axis, one at around 30 and the other around 70, each with frequencies of up to about 25 on the y-axis.
  • A histogram displaying frequencies on the y-axis and data ranges from 0 to 100 on the x-axis. The highest bar is near the 20-30 range, with a tail toward the higher end of the x-axis.

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3
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Which of the following options correctly orders the histograms shown below, from the histogram with the greatest proportion of data below its mean to the histogram with the smallest proportion of data below its mean?

Three histograms labeled A, B, and C. Histogram A has a positively skewed distribution, histogram B has a negatively skewed distribution, and histogram C has an approximately normal distribution.

  • A, B, and C have the same proportion of data below their respective means.

  • A, B, C

  • A, C, B

  • B, A, C

  • C, B, A

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4
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The test scores of two classes are shown in the back-to-back stemplot below.

A back-to-back stemplot for the test scores of classes A and B. Class A has a concentration of scores in the 40s and 50s, which tapers off toward the high end of scores. Class B has fewer data items, which are more spread out. Class B's scores peak in the 20s and 30s and tail off toward the high end of scores.

Which of the following statements is true about the distribution of scores?

  • The distribution of test scores for class A is skewed to the left, and the distribution of test scores for class B is skewed to the right.

  • The distribution of test scores for class A is skewed to the right, and the distribution of test scores for class B is skewed to the left.

  • The distribution of test scores for both classes is symmetric.

  • The distribution of test scores for both classes is skewed to the left.

  • The distribution of test scores for both classes is skewed to the right.

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5
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A librarian investigated the number of words used in the library's books. She found that in the children's section, the number of words per book followed a positively skewed distribution, ranging from 0 to 20,000 words with a mean of 500 words. In the adult section, the number of words per book followed an approximately normal distribution, centered around 80,000 words and ranging from 20,000 to 140,000 words. There are approximately the same number of books for children and adults in the library. Which of the following best describes a histogram of the number of words per book across all 100,000 books in the library?

  • Bimodal

  • Approximately normal and centered at 40,250

  • Approximately uniform and centered at 40,250

  • Positively skewed

  • Negatively skewed

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