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AP®StatisticsCollege BoardExam QuestionsUnit 1: Exploring One-Variable DataSummary Statistics

Summary Statistics (College Board AP® Statistics)

Exam Questions

5 mins5 questions
1
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A random sample of 522 acorns was collected, and the weight of each acorn was measured. According to the boxplot below, what is the approximate interquartile range (IQR) of the weights?

Boxplot showing weight distribution for the weights of a sample of acorns.

  • 2.5

  • 1.5

  • 1

  • 12

  • 9.5

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2
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The time, in minutes, for 160 runners to complete a marathon is summarized in the frequency table below.

Time, t, (minutes)

Frequency

180 less than t less or equal than 216

4

216 less than t less or equal than 252

13

252 less than t less or equal than 288

59

288 less than t less or equal than 324

65

324 less than t less or equal than 360

19

Which of the following statements about the median time is true?

  • It is less than 180 minutes.

  • It is greater than 216 minutes but less than or equal to 252 minutes.

  • It is greater than 252 minutes but less than or equal to 288 minutes.

  • It is greater than 288 minutes but less than or equal to 324 minutes.

  • It is greater than or equal to 360 minutes.

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3
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The selling prices of 25 houses sold by one particular realtor over a five-year period are shown in the frequency table below.

Price (in thousands of $)

250

275

300

325

350

375

400

425

Frequency

1

6

3

3

2

5

3

2

Which of the following best describes the shape of the distribution of selling prices that the realtor managed to obtain?

  • Uniform

  • Bimodal

  • Approximately normal

  • Skewed to the left (negatively skewed)

  • Skewed to the right (positively skewed)

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4
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The number of books borrowed from a library in a day was recorded for each of the last ten days by the librarian. Summary measures are shown below.

Min = 6

Max = 29

Lower quartile = 17

Upper quartile = 22

Median = 20

n = 10

Which of the following statements are true?

  • The largest observation is 29, and it is an outlier. No other observations in the data set could be outliers.

  • The smallest observation is 6, and it is an outlier. No other observations in the data set could be outliers.

  • Both 6 and 29 are outliers. It is possible that there are other outliers.

  • 29 is an outlier, and it is possible that there are other outliers at the high end of the data set. There are no outliers at the low end of the data set.

  • 6 is an outlier, and it is possible that there are other outliers at the low end of the data set. There are no outliers at the high end of the data set.

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5
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Data is collected on the earnings of individuals in a global company. The distribution of the data is skewed to the right. Which of the following statements is the most reasonable conclusion about the earnings of individuals based on the data?

  • There are a greater number of individuals that earn more than the mean than there are that earn less than the mean.

  • The median value is the average of the first quartile and the third quartile.

  • There are a greater number of individuals between the first quartile and the median than there are between the median and the third quartile.

  • The mean is less than the median.

  • The value of the first quartile minus the minimum is less than the value of the maximum minus the third quartile.

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