AP Statistics Unit 1: Exploring One-Variable Data Practice Exam

Assessment for Unit 1: Exploring One-Variable Data

Estimated Time: 60 minutes

Exam Details

Questions: 30 total (30 multiple choice)
Time: 60 minutes (recommended)
Topics Covered: Unit 1: Exploring One-Variable Data
Format: Multiple Choice questions matching real exam difficulty
Scoring: Instant results with detailed explanations

A. Multiple-Choice Questions (30 Questions)

Select the one best answer for each question.

1. A team of researchers is conducting a study on the health of coral reefs off the coast of Australia. For each of 50 distinct reef locations, they record the water temperature (in degrees Celsius), the percentage of coral bleaching, the dominant species of coral present, and the depth of the reef (in meters). Which of the following identifies the individuals in this study?

(A)The researchers conducting the study.(B)The 50 distinct reef locations.(C)The water temperature and depth.(D)The dominant species of coral.

2. A university registrar maintains a database of student information. The database includes the following variables for each student: Grade Point Average (GPA), Major, Student ID Number, and Annual Tuition Paid (in dollars). Which of the following correctly classifies these variables?

(A)GPA and Annual Tuition Paid are quantitative; Major and Student ID Number are categorical.(B)GPA, Student ID Number, and Annual Tuition Paid are quantitative; Major is categorical.(C)GPA is quantitative; Major, Student ID Number, and Annual Tuition Paid are categorical.(D)All four variables are quantitative because they can be described by numbers or values.

3. A manufacturing plant produces steel rods. A quality control engineer records the following data for a sample of rods: the production shift (Morning, Afternoon, Night), the number of surface defects detected, the length of the rod (in centimeters), and the diameter of the rod (in millimeters). Which variable in this dataset is best classified as a discrete quantitative variable?

(A)Production shift(B)Number of surface defects(C)Length of the rod(D)Diameter of the rod

4. A student finds a scrap of paper with the following list of numbers: 12, 15, 11, 16, 13. The student attempts to calculate the mean and standard deviation to analyze the distribution. Which of the following best explains why a complete statistical analysis is not possible based solely on these numbers?

(A)The sample size is too small to calculate a valid mean.(B)The numbers are not ordered from least to greatest.(C)The data lacks context, such as the variable being measured and the units.(D)There is no indication of whether the data comes from a random sample.

5. The distribution of heights for adult giraffes is approximately normal with mean $\mu_G$ and standard deviation $\sigma_G$. The distribution of heights for adult elephants is approximately normal with mean $\mu_E$ and standard deviation $\sigma_E$. A graph of the two distributions shows that the curve for giraffes is centered at a higher value than the curve for elephants, but the curve for elephants is wider and flatter than the curve for giraffes. Which of the following statements must be true?

(A)$\mu_G > \mu_E$ and $\sigma_G > \sigma_E$(B)$\mu_G > \mu_E$ and $\sigma_G < \sigma_E$(C)$\mu_G < \mu_E$ and $\sigma_G > \sigma_E$(D)$\mu_G < \mu_E$ and $\sigma_G < \sigma_E$

6. Raul took two different college entrance exams. On the Math Level 1 exam, the mean score was 50 with a standard deviation of 10. Raul scored 65. On the Math Level 2 exam, the mean score was 150 with a standard deviation of 25. Raul scored 180. Assuming both distributions of scores are approximately normal, on which exam did Raul perform better relative to the other test-takers?

(A)Level 1, because his z-score is 1.5, which is higher than his z-score of 1.2 on Level 2.(B)Level 2, because his score of 180 is significantly higher than his score of 65.(C)Level 2, because his z-score is 1.2, which indicates he is in a higher percentile than Level 1.(D)He performed equally well on both exams because he scored 15 points above the mean on Level 1 and 30 points above the mean on Level 2.

7. The lifespan of a certain brand of light bulb is approximately normally distributed with a mean of 1,200 hours and a standard deviation of 50 hours. Based on the Empirical Rule (68-95-99.7 rule), approximately what percent of these light bulbs will last between 1,100 hours and 1,300 hours?

(A)68%(B)95%(C)99.7%(D)34%

8. A specialized scale is used to weigh packages at a distribution center. The weights of the packages are normally distributed with a mean of 24.0 kg and a standard deviation of 1.5 kg. The distribution center manager wants to identify the heaviest 10% of packages for special handling. What is the minimum weight, in kg, for a package to be included in the heaviest 10%?

(A)22.08 kg(B)25.28 kg(C)25.92 kg(D)26.47 kg

9. [Skill: 2.A | Topic: 1.2] A biologist is studying a population of 40 gopher tortoises in a Florida state park to understand their health and distribution. For each tortoise, the biologist records the shell length (in centimeters), the weight (in kilograms), the sex (male or female), and the burrow location ID number. Which of the following represents the individuals in this study?

(A)The 40 gopher tortoises(B)The shell length, weight, sex, and burrow location ID(C)The Florida state park(D)The biologist conducting the study

10. [Skill: 2.A | Topic: 1.2] A marketing firm collects data on customers who purchased a new vehicle in the last month. The variables recorded for each customer are: Age (years), Annual Income (dollars), Zip Code of residence, and Number of vehicles owned. Which of the following is a categorical variable?

(A)Age(B)Annual Income(C)Zip Code(D)Number of vehicles owned

11. [Skill: 2.A | Topic: 1.2] A local bakery tracks daily production metrics to optimize efficiency. Which of the following variables recorded by the bakery is a quantitative variable that is discrete?

(A)The exact weight of flour used in kilograms(B)The temperature of the oven in degrees Celsius(C)The number of baguettes burnt during baking(D)The type of pastry with the highest sales volume

12. [Skill: 2.A | Topic: 1.2] The table below displays data for a sample of roller coasters at an amusement park. | Coaster Name | Max Height (ft) | Top Speed (mph) | Inversions (Yes/No) | Track Material | | :--- | :--- | :--- | :--- | :--- | | The Falcon | 120 | 55 | Yes | Steel | | Timber Wolf | 95 | 48 | No | Wood | | Velocity | 205 | 72 | Yes | Steel | | The Twister | 150 | 60 | Yes | Steel | Which statement correctly classifies the variables "Top Speed" and "Track Material"?

(A)Both Top Speed and Track Material are categorical variables.(B)Both Top Speed and Track Material are quantitative variables.(C)Top Speed is a categorical variable, and Track Material is a quantitative variable.(D)Top Speed is a quantitative variable, and Track Material is a categorical variable.

13. A high school administration surveyed 250 students to determine their primary mode of transportation to school. The counts for each category are displayed in the frequency table below. | Mode of Transportation | Number of Students | | :--- | :---: | | Bus | 110 | | Car | 80 | | Walk | 40 | | Bicycle | 20 | | **Total** | **250** | Which of the following values represents the relative frequency of students who use non-motorized transportation (Walk or Bicycle)?

(A)0.24(B)0.32(C)0.60(D)60

14. A market researcher is analyzing customer satisfaction for two different streaming services, Service A and Service B. The data is collected from two different sample groups. * **Service A:** Sample size $n = 200$. 120 customers reported being 'Highly Satisfied'. * **Service B:** Sample size $n = 1,000$. 500 customers reported being 'Highly Satisfied'. Which of the following statements correctly compares the frequency and relative frequency of 'Highly Satisfied' customers for the two services?

(A)Service B has a higher frequency and a higher relative frequency of 'Highly Satisfied' customers than Service A.(B)Service A has a higher frequency and a higher relative frequency of 'Highly Satisfied' customers than Service B.(C)Service B has a higher frequency, but Service A has a higher relative frequency of 'Highly Satisfied' customers.(D)The relative frequencies cannot be compared because the sample sizes are different.

15. A local library tracks the genres of books borrowed during a single week. The relative frequencies for the top four genres are shown in the table below. All other genres are grouped into 'Other'. | Genre | Relative Frequency | | :--- | :---: | | Mystery | 0.35 | | Sci-Fi | 0.25 | | Romance | 0.20 | | Biography | 0.10 | | Other | 0.10 | Based on the table, which of the following claims is supported by the data?

(A)More people borrowed Sci-Fi books than Romance and Biography books combined.(B)Exactly 35 people borrowed Mystery books.(C)The number of people who borrowed Mystery books is greater than the number of people who borrowed Sci-Fi books.(D)The 'Other' category contains the fewest number of borrowed books among all specific genres listed.

16. An environmental science class categorized the type of waste found in a school cafeteria's recycle bins. The total weight of the waste analyzed was 50 kilograms. The data is summarized below: * **Paper:** Relative Frequency = 0.40 * **Plastic:** Frequency = 15 kg * **Aluminum:** Frequency = ? * **Glass:** Relative Frequency = 0.10 If these are the only four categories, what is the frequency (in kg) of Aluminum waste?

(A)0.20 kg(B)5 kg(C)10 kg(D)20 kg

Refer to the figure below.

17. A high school administration wants to compare the transportation methods of Grade 9 students versus Grade 12 students. They survey a random sample of students from each grade. The results are shown in the side-by-side bar chart below. Based on the graph, which of the following is the best conclusion?

(A)Grade 12 students are more likely to take a car to school than Grade 9 students.(B)The number of Grade 9 students who walk is the same as the number of Grade 12 students who walk.(C)Bus is the most popular mode of transportation for both grades.(D)Because the frequency of car riders is the same for both grades, there is no association between grade level and taking a car.

18. A marketing firm conducts a survey to determine the favorite soft drink flavor among a group of 200 teenagers. The data is displayed in a relative frequency bar chart. The bar for 'Cola' has a height of 0.35, and the bar for 'Lemon-Lime' has a height of 0.25. Which of the following calculations correctly determines the number of teenagers who chose either Cola or Lemon-Lime?

(A)(0.35 + 0.25) / 200(B)(0.35 + 0.25) * 200(C)(0.35 * 200) + 0.25(D)200 / (0.35 + 0.25)

19. A newspaper publishes a bar chart comparing the approval ratings of two local politicians, Politician A and Politician B. The bar for Politician A reaches 42% and the bar for Politician B reaches 44%. However, the vertical axis (y-axis) of the graph starts at 40% and ends at 45%. Which of the following best describes a misleading feature of this graph?

(A)The graph violates the area principle because the width of the bars is not consistent.(B)The graph is misleading because it uses percentages instead of frequencies.(C)The graph exaggerates the difference in approval ratings between the two politicians.(D)The graph is misleading because a pie chart would be more appropriate for comparing two categories.

20. [Skill: 2.A | Topic: 1.2] A veterinary researcher collects the following data on a sample of domestic cats: 1. **Body Length:** Measured in centimeters from nose to tail tip. 2. **Number of Toes:** A count of the total toes on all paws. 3. **Coat Pattern:** Classified as Tabby, Solid, Calico, or Tortoiseshell. 4. **Microchip ID:** A unique 15-digit identification number. Which of the variables listed above is classified as a **discrete quantitative** variable?

(A)Body Length(B)Number of Toes(C)Coat Pattern(D)Microchip ID

21. [Skill: 2.A | Topic: 1.3] A histogram summarizes the heights (in inches) of 50 cherry trees in an orchard. The bins have a width of 5 inches, starting at 60 inches (e.g., 60 to <65). The frequencies for the bins are provided below: * **60 to <65:** 3 trees * **65 to <70:** 7 trees * **70 to <75:** 10 trees * **75 to <80:** 20 trees * **80 to <85:** 10 trees Based on the distribution described, which of the following statements correctly describes the shape of the distribution and the interval containing the median height?

(A)The distribution is skewed left, and the median is in the interval 70 to <75.(B)The distribution is skewed left, and the median is in the interval 75 to <80.(C)The distribution is skewed right, and the median is in the interval 70 to <75.(D)The distribution is roughly symmetric, and the median is in the interval 75 to <80.

22. A gathered dataset represents the commute times, in minutes, for 40 employees at a large corporation. The histogram of the data is unimodal and skewed to the right. Which of the following statements best describes the relationship between the mean and the median of this distribution?

(A)The mean is approximately equal to the median.(B)The mean is less than the median.(C)The mean is greater than the median.(D)The relationship between the mean and median cannot be determined from the shape of the distribution alone.

23. A teacher records the scores of a difficult physics exam. The histogram of the exam scores shows two distinct peaks, one centered around a score of 40 and another centered around a score of 85, with very few scores between 55 and 70. Which of the following best describes the shape of this distribution?

(A)Unimodal and symmetric(B)Bimodal with a gap(C)Uniform and symmetric(D)Skewed left with outliers

24. A real estate agent analyzes the sale prices of 50 recently sold homes in a specific neighborhood. The histogram of the sale prices shows a distribution that is strongly skewed to the right. Which of the following statements correctly compares the mean and the median of the sale prices?

(A)The mean is less than the median.(B)The mean is approximately equal to the median.(C)The mean is greater than the median.(D)The relationship between the mean and median cannot be determined without the raw data.

25. A botanist collects two sets of data regarding the heights (in centimeters) of seedlings in two different environments. The data sets are listed below. Set A: 12, 14, 15, 16, 18 Set B: 12, 12, 15, 18, 18 Both data sets have a mean of 15 cm and a range of 6 cm. Which of the following statements correctly compares the standard deviations of the two data sets?

(A)The standard deviation of Set A is equal to the standard deviation of Set B.(B)The standard deviation of Set A is greater than the standard deviation of Set B.(C)The standard deviation of Set B is greater than the standard deviation of Set A.(D)The standard deviations cannot be compared without calculating the variance first.

26. The five-number summary for a dataset representing the daily commute times (in minutes) for employees at a large corporation is given below: Minimum: 15 First Quartile (Q1): 35 Median: 45 Third Quartile (Q3): 55 Maximum: 90 Using the 1.5 × IQR rule, which of the following correctly describes the outliers in this dataset?

(A)There are no outliers in the dataset.(B)There is at least one high outlier, but no low outliers.(C)There is at least one low outlier, but no high outliers.(D)There is at least one low outlier and at least one high outlier.

Refer to the figure below.

27. [Skill: 2.A | Topic: 1.8] A botanist collects data on the heights, in centimeters, of a random sample of 200 saplings in a nursery. The data is summarized in the boxplot below. Based on the boxplot, which of the following is the best estimate for the number of saplings with heights between 18 cm and 30 cm?

(A)24(B)50(C)100(D)122

28. [Skill: 3.A | Topic: 1.8] The five-number summary for a dataset of annual household incomes in a small town is given below: Minimum: 25,000 dollars First Quartile (Q1): 42,000 dollars Median: 58,000 dollars Third Quartile (Q3): 70,000 dollars Maximum: 115,000 dollars Using the 1.5 x IQR rule for outliers, which of the following statements is true regarding outliers in this dataset?

(A)There are no outliers in the dataset.(B)There is at least one outlier on the low end, but no outliers on the high end.(C)There is at least one outlier on the high end, but no outliers on the low end.(D)There are outliers on both the low end and the high end.

29. [Skill: 2.D | Topic: 1.8] A statistics student constructs a boxplot for a set of data representing the time, in minutes, it takes students to complete a puzzle. The boxplot shows that the distance from the minimum to the median is significantly smaller than the distance from the median to the maximum. Additionally, the distance from Q1 to the median is smaller than the distance from the median to Q3. Based on this description, which of the following statements is most likely true about the relationship between the mean and the median of the distribution?

(A)The mean is approximately equal to the median because the distribution is symmetric.(B)The mean is less than the median because the distribution is skewed to the left.(C)The mean is greater than the median because the distribution is skewed to the right.(D)The mean is greater than the median because the distribution is skewed to the left.

30. A school district collected data on the years of teaching experience for teachers at two different high schools, High School East and High School West. The summary statistics are provided in the table below. | School | Mean | Median | Standard Deviation | Min | Max | | :--- | :--- | :--- | :--- | :--- | :--- | | East | 12.5 | 12.0 | 3.2 | 2 | 25 | | West | 18.4 | 14.5 | 6.8 | 1 | 40 | Based on the summary statistics, which of the following conclusions is best supported?

(A)The distribution of teaching experience at High School East is likely skewed right, while High School West is roughly symmetric.(B)The distribution of teaching experience at High School West is likely skewed right, while High School East is roughly symmetric.(C)High School East has more variability in teaching experience than High School West.(D)A teacher with 13 years of experience would be in the top 25% of experience at High School East.

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