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AP Stats

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Unit 1

1.12 MC Answers and Review

6 min read•december 4, 2021

AP Statistics 📊

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Answers and Review for Multiple Choice Practice on Exploring One-Variable Data

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⛔STOP ⛔ Before you look at the answers make sure you gave this practice quiz a try so you can assess your understanding of the concepts covered in Unit 1. Click here for the practice questions: AP Statistics Unit 1 Multiple Choice Questions.

Facts about the test: The AP Statistics exam has 40 multiple choice questions and you will be given 1 hour 30 minutes to complete the section. That means it should take you around 11 minutes to complete 5 questions.

The following questions were not written by College Board and although they cover information outlined in the AP Statistics Course and Exam Description the formatting on the exam may be different.

1. If we are looking at a boxplot and notice that the distribution is skewed right, what measure of center should we use?

A. Mean

B. Median

C. Mode

D. IQR

Answer: Anytime a distribution is skewed, we should use the median as our measure of center and the IQR as our measure of spread. When it is symmetric, we should use mean and standard deviation.

📄 Study AP Stat, Unit 1.6: Describing the Distribution of a Quantitative Variable

2. A researcher has gathered the number of soft drinks teenagers drink on a daily basis by taking a random sample of 1500 teenagers from around the world. We find that our data shows that the mean is larger than the median. What does this tell us about the shape of the distribution?

A. Skewed Right

B. Skewed Left

C. Symmetric

D. Uniform

Answer: Anytime the mean or median are not equal, the mean is going to be closer to the tail. Since the mean is greater than the median in this example, the mean is further to the left, hence the tail is further to the left and the distribution is skewed right. (always skewed in the direction of where the tail is)

📄 Study AP Stat, Unit 1.6: Describing the Distribution of a Quantitative Variable

3. To find out the color preference of residents at a local retirement community, the president asks each of the residents what their favorite color is. What type of variable is this?

A. Quantitative Variable

B. Quasimodal Variable

C. Dimensional Variable

D. Categorical Variable

Answer: Since someone's favorite color fits into a category and can't be "averaged", this is categorical. There is not such thing as quasimodal or dimensional variables.

📄 Study AP Stat, Unit 1.2: The Language of Variation: Variables

4. Given the five number summary below, find the IQR. 5, 8, 10, 14, 26

A. 6

B. 9

C. 10

D. 21

Answer: To find the IQR, we subtract the Q3 (14) and the Q1 (8), which is 6. The incorrect answers are 21 (range), 10 (median) and 9, which is some sort of "adjusted range" taking out the obvious outlier of 26.

📄 Study AP Stat, Unit 1.7: Summary Statistics for a Quantitative Variable

5. If the mean and median of a distribution are equal, what does this tell us about the shape?

A. Skewed Right

B. Skewed Left

C. Symmetric

D. Unimodal

Answer: When the mean and median are equal in a distribution, this tells us that the distribution is symmetric. A good example of this is the normal distribution.

📄 Study AP Stat, Unit 1.7: Summary Statistics for a Quantitative Variable

6. We are given a distribution that is symmetric, what measure of spread should we use?

A. Mean

B. Mode

C. Standard Deviation

D. IQR

Answer: When a distribution is symmetric, we should use the mean for our measure of center and standard deviation for our measure of spread.

📄 Study AP Stat, Unit 1.6: Describing the Distribution of a Quantitative Variable

7. Which of the following is not a part of the describing/comparing distribution process?

A. Units

B. Center

C. Spread

D. Shape

Answer: While units are an important part of including context in your answer, it is not required to describe or compare distributions. If you are using the CUSS process, the U stands for unusual features (like outliers or gaps).

📄 Study AP Stat, Unit 1.7: Summary Statistics for a Quantitative Variable

8. What do we call a numerical summary of sample data?

A. Parameter

B. Statistic

C. Percentile

D. Quartile

Answer: When we are working with a numerical summary that came from a sample, we are dealing with a statistic. When it is a numerical summary from a population, then we have a parameter

📄 Study AP Stat, Unit 1.7: Summary Statistics for a Quantitative Variable

9. Doctors often compare someone's height and weight to worldwide, or nationwide averages. If doctors were to convert the height measurements from feet to meters, how would the center and spread change?

A. Neither center nor spread would change.

B. The center would not change, but the spread would change.

C. The center would change, but the spread would not.

D. The center would change with the conversion factor as well as the spread.

Answer: When we change units, we are either multiplying or dividing by a conversion factor. When multiplying or dividing, this changes both the center and spread.

📄 Study AP Stat, Unit 1.7: Summary Statistics for a Quantitative Variable

10. How do we determine an upper outlier of a distribution?

A. Mean + 3(IQR)

B. Median + 3(IQR)

C. Maximum - 0.5 (IQR)

D. Q3+1.5(IQR)

Answer: The formula to determine outliers is Q3+1.5(IQR) and Q1-1.5(IQR). It is also sometimes acceptable to use Mean + 3 (SD).

📄 Study AP Stat, Unit 1.8: Graphical Representations of Summary Statistics

11. Which of the following do we not get in a boxplot?

A. Mean

B. Median

C. Maximum

D. Minimum

Answer: A boxplot displays the 5 number summary of a distribution which is the minimum, Q1, Median, Q3, and maximum.

📄 Study AP Stat, Unit 1.8: Graphical Representations of Summary Statistics

12. Which of the following is a specification of the normal distribution?

A. Small Range

B. Bimodal

C. Symmetric

D. Skewed Right

Answer: A normal distribution is symmetric, mound shaped, unimodal and is used to represent many data sets in our world.

📄 Study AP Stat, Unit 1.10: The Normal Distribution

13. The empirical rule states that the normal distribution contains 99.7% of the data between how many standard deviations?

A. 1

B. 2

C. 3

D. 10

Answer: The empirical rule states that the normal distribution follows the 68-95-99.7 rule, where 68% of the data is within 1 standard deviation of the mean, 95% within 2 and 99.7% within 3.

📄 Study AP Stat, Unit 1.10: The Normal Distribution

14. A local office manager is gathering data about each of the employees and their work necessities. Which of the following is a quantitative variable?

A. Apple or Windows Preference

B. Amount of hours worked each month

C. iPhone or android preference

D. Music preference for office speakers

Answer: Amount of hours worked is a quantitative variable because it measures something that can be averaged among all employees. The other options do not give us a data set that is "averageable"

📄 Study AP Stat, Unit 1.2: The Language of Variation: Variables

15. Which type of chart is best for displaying a categorical variable?

A. Dot Plot

B. Box Plot

C. Stem and Leaf Plot

D. Pie Chart

Answer: A pie chart is best for categorical variable because it will display different proportions, where dot plot, box plot and stem and leaf plot shows quantities for each of our subjects rather than where they call in a category.

📄 Study AP Stat, Unit 1.4: Representing a Categorical Variable with Graphs

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