Chapter 10: Distributions and Associations

Test Bank

Multiple Choice

1. What does the term “descriptive statistics” refer to?

A. trends in population data

B. description of metadata

C. patterns in the sample data

D. regression analysis

Learning Objective: 10-1: Choose and interpret basic statistics to describe distribution of values of a single variable (univariate statistics).

Cognitive Domain: Knowledge

Answer Location: Introduction

Difficulty Level: Medium

2. A report shows the mean, median, mode of a quantitative variable. It also gives the range, standard deviation, skewness and kurtosis values for the variable. What is this type of report called?

A. univariate summary statistics

B. bivariate statistics

C. quantitative description

D. statistical summary

Learning Objective: 10-1: Choose and interpret basic statistics to describe distribution of values of a single variable (univariate statistics).

Cognitive Domain: Comprehension

Answer Location: Distributions of Single Variables

Difficulty Level: Medium

3. What is the median value of the following set of numbers: 2, 5, 17, 1, 11, 18?

A. 9.5

B. 8

C. 17.5

D. 5

Learning Objective: 10-1: Choose and interpret basic statistics to describe distribution of values of a single variable (univariate statistics).

Cognitive Domain: Application

Answer Location: Median

Difficulty Level: Easy

4. What type of distribution would you call the following set of numbers, in terms of measures of central tendency: 23, 25, 25, 41, 25, 50, 47, 50, 21, 50?

A. multi-modal

B. uniform

C. normal

D. bimodal

Learning Objective: 10-1: Choose and interpret basic statistics to describe distribution of values of a single variable (univariate statistics).

Cognitive Domain: Application

Answer Location: Mode

Difficulty Level: Easy

5. When presenting a frequency distribution of a variable in a sample, why is it important to show percentage of cases for each value of the variable?

A. for ease of understanding

B. to correct for sample size

C. to show a common scale

D. in order to show a histogram

Learning Objective: 10-1: Choose and interpret basic statistics to describe distribution of values of a single variable (univariate statistics).

Cognitive Domain: Knowledge

Answer Location: Frequency Distribution

Difficulty Level: Medium

6. What does the term “composition” refer to? Choose the best answer.

A. how the categories of a variable are spread across all categories

B. the measurement level of a variable in a given sample

C. how distinct values or categories of a variable make up the sample

D. values for central tendency of a set of numbers

Learning Objective: 10-1: Choose and interpret basic statistics to describe distribution of values of a single variable (univariate statistics).

Cognitive Domain: Knowledge

Answer Location: Frequency Distribution

Difficulty Level: Medium

7. How is the range of a continuous variable calculated?

A. largest minus smallest value plus one

B. largest minus smallest value

C. largest minus smallest value minus one

D. largest value of the variable minus one

Learning Objective: 10-1: Choose and interpret basic statistics to describe distribution of values of a single variable (univariate statistics).

Cognitive Domain: Knowledge

Answer Location: Range

Difficulty Level: Easy

8. Which of the following statements are true regarding the term “interquantile range”?

A. It shows the range of each quantile of a distribution.

B. It captures the middle 50% of a ranked distribution.

C. It can be used as an alternative to the mode.

D. It gives the upper and lower limits of the median.

Learning Objective: 10-1: Choose and interpret basic statistics to describe distribution of values of a single variable (univariate statistics).

Cognitive Domain: Comprehension

Answer Location: Range

Difficulty Level: Medium

9. The sum of the squared deviations from the mean of 20 values is 1750. What is the standard deviation of these values?

A. 41.59

B. 87.50

C. 9.00

D. 9.35

Learning Objective: 10-1: Choose and interpret basic statistics to describe distribution of values of a single variable (univariate statistics).

Cognitive Domain: Application

Answer Location: Variance

Difficulty Level: Easy

10. How would you define the term “outlier”? Choose the best answer

A. value that is greater than a defined range of values of a variable

B. value significantly higher or lower than the next adjacent value of a variable

C. value that is smaller than the minimum value of a variable

D. value that is higher than the 50th percentile of a quantitative variable

Learning Objective: 10-1: Choose and interpret basic statistics to describe distribution of values of a single variable (univariate statistics).

Cognitive Domain: Knowledge

Answer Location: Standard Deviation

Difficulty Level: Medium

11. The shape of a distribution has a skewness value of –12.5. What can you say about the magnitude of the mean relative to the median of this distribution?

A. Mean is lower than the median.

B. Mean and median are equal.

C. Mean is greater than the median.

D. Mean is 0 and median is negative.

Learning Objective: 10-1: Choose and interpret basic statistics to describe distribution of values of a single variable (univariate statistics).

Cognitive Domain: Application

Answer Location: Shape

Difficulty Level: Medium

12. Which measure of central tendency is preferred to describe a distribution that is significantly skewed?

A. mean

B. variance

C. median

D. mode

Learning Objective: 10-1: Choose and interpret basic statistics to describe distribution of values of a single variable (univariate statistics).

Cognitive Domain: Knowledge

Answer Location: Shape

Difficulty Level: Easy

13. The mean and standard deviation of a distribution is 32.8 and 7.5, respectively. What is the z score of the number 70.6 in this distribution?

A. 4.37

B. 37.8

C. 9.41

D. 5.04

Learning Objective: 10-1: Choose and interpret basic statistics to describe distribution of values of a single variable (univariate statistics).

Cognitive Domain: Application

Answer Location: Position in a Distribution

Difficulty Level: Medium

14. What does the z-score represent for a number in a roughly normal distribution?

A. how many standard deviations above or below the mean

B. number of variance units away from the mean

C. an absolute value without a unit of measurement

D. the absolute distance from the mean of a distribution

Learning Objective: 10-1: Choose and interpret basic statistics to describe distribution of values of a single variable (univariate statistics).

Cognitive Domain: Comprehension

Answer Location: Position in a Distribution

Difficulty Level: Hard

15. What are the plausible values possible for the standard deviation of any distribution?

A. positive or negative values

B. negative values

C. positive values

D. positive or zero

Learning Objective: 10-2: Assess plausibility of univariate statistical results.

Cognitive Domain: Knowledge

Answer Location: Plausibility Criteria for Univariate Statistics

Difficulty Level: Easy

16. Which of the following correctly characterize the plausibility of Z-scores of a distribution calculated using the sample mean and deviation?

A. They must all be positive.

B. They must be positive and negative.

C. They must fall within –3 and +3.

D. 67% of scores must be positive.

Learning Objective: 10-2: Assess plausibility of univariate statistical results.

Cognitive Domain: Knowledge

Answer Location: Plausibility Criteria for Univariate Statistics

Difficulty Level: Medium

17. An ordinal variable called AGE GROUP contains five possible classes starting from “18–25” years, and a maximum class of “60–70” years. In addition to a frequency distribution, which measure of central tendency could be shown in presenting exploratory analysis results of the variable?

A. median

B. mean

C. range

D. mode

Learning Objective: 10-3: Design and read tables and charts to display distributions.

Cognitive Domain: Comprehension

Answer Location: Portraying Distribution of Categorical Variables

Difficulty Level: Medium

18. Which of the following is considered the best way to present data (in charts) of a nominal variable?

A. pie chart

B. line chart

C. histogram

D. vertical bars

Learning Objective: 10-3: Design and read tables and charts to display distributions.

Cognitive Domain: Comprehension

Answer Location: Nominal Variables

Difficulty Level: Easy

19. In a box-and-whiskers plot of an interval variable, what do the lower and upper lines of the box represent?

A. the mean and the median values

B. the first and third quantile values

C. the minimum and maximum values

D. the second and third quantile values

Learning Objective: 10-3: Design and read tables and charts to display distributions.

Cognitive Domain: Knowledge

Answer Location: Portraying Distribution of Categorical Variables

Difficulty Level: Medium

20. The correlation coefficient between a dependent and an independent variable is –0.4. What can we say about association between the two variables?

A. the association is positive

B. the association is not significant

C. the association is weak and positive

D. the association is inverse

Learning Objective: 10-4: Select and interpret statistics to describe the relationship between two variables (bivariate statistics).

Cognitive Domain: Knowledge

Answer Location: Correlation

Difficulty Level: Easy

21. Which of the following could be used to present association between two categorical variables?

A. cross-tab

B. histogram

C. stacked bar chart

D. frequency table

Learning Objective: 10-4: Select and interpret statistics to describe the relationship between two variables (bivariate statistics).

Cognitive Domain: Comprehension

Answer Location: Cross-Tabulation

Difficulty Level: Easy

22. In a study, the number of cigarettes smoked by high school students was analyzed in relation to several social factors. The primary factor was found to be peer pressure, which was categorized as low, medium, and, high for the study. What kind of test would you do to find the association between peer pressure and smoking?

A. correlation coefficient

B. difference in means

C. analysis of variance

D. R² test

Learning Objective: 10-4: Select and interpret statistics to describe the relationship between two variables (bivariate statistics).

Cognitive Domain: Application

Answer Location: Difference in Means or ANOVA

Difficulty Level: Hard

23. A 2-way ANOVA measure is used to identify association between which type of variables?

A. categorical dependent and two continuous variables taken together

B. continuous dependent and two continuous independent variables

C. categorical dependent, one continuous and one nominal variable

D. continuous dependent and two categorical variables taken together

Learning Objective: 10-6: Identify methods used to describe associations among three variables.

Cognitive Domain: Knowledge

Answer Location: Two-Way Difference in Means or 2-Way ANOVA

Difficulty Level: Medium

24. What are the plausible limits to values of coefficient of determination?

A. –1 to +1

B. 0 to +1

C. –1 to 0

D. –1 < to <+1

Learning Objective: 10-7: Assess plausibility of bivariate and three-way results.

Cognitive Domain: Knowledge

Answer Location: Plausibility Criteria for Bivariate and Three-Way Statistics

Difficulty Level: Easy

25. What are the plausible limits to the results from an ANOVA test?

A. lowest and highest value of independent variable

B. minimum and maximum value of the outcome variable

C. minimum of dependent and maximum of independent variable

D. lowest value of independent and highest value of outcome

Learning Objective: 10-7: Assess plausibility of bivariate and three-way results.

Cognitive Domain: Knowledge

Answer Location: Plausibility Criteria for Bivariate and Three-Way Statistics

Difficulty Level: Easy

True/False

1. Statistical methods refer to techniques used to describe, organize, and, interpret data.

Learning Objective: 10-1: Choose and interpret basic statistics to describe distribution of values of a single variable (univariate statistics).

Cognitive Domain: Knowledge

Answer Location: Introduction

Difficulty Level: Easy

2. Shape refers to how much values of a variable differ from one another.

Learning Objective: 10-1: Choose and interpret basic statistics to describe distribution of values of a single variable (univariate statistics).

Cognitive Domain: Knowledge

Answer Location: Distributions of Single Variables

Difficulty Level: Easy

3. Median is the 50th percentile value of a variable whose values have been sorted from lowest to highest value.

Learning Objective: 10-1: Choose and interpret basic statistics to describe distribution of values of a single variable (univariate statistics).

Cognitive Domain: Knowledge

Answer Location: Median

Difficulty Level: Easy

4. The values of a numeric variable were as follows: 148, 120, 91, 178, 202, 115, and, missing. The mean value of the variable is 142.33.

Learning Objective: 10-1: Choose and interpret basic statistics to describe distribution of values of a single variable (univariate statistics).

Cognitive Domain: Application

Answer Location: Mean

Difficulty Level: Medium

5. A distribution with two modal values is called a multimodal distribution.

Learning Objective: 10-1: Choose and interpret basic statistics to describe distribution of values of a single variable (univariate statistics).

Cognitive Domain: Knowledge

Answer Location: Mode

Difficulty Level: Easy

6. The frequency distribution of a continuous variable with many unique values should be presented in a chart, rather than in a table.

Learning Objective: 10-1: Choose and interpret basic statistics to describe distribution of values of a single variable (univariate statistics).

Cognitive Domain: Knowledge

Answer Location: Frequency Distribution

Difficulty Level: Easy

7. The variability in a nominal variable could be shown by a frequency distribution or by the range measure.

Learning Objective: 10-1: Choose and interpret basic statistics to describe distribution of values of a single variable (univariate statistics).

Cognitive Domain: Knowledge

Answer Location: Frequency Distribution

Difficulty Level: Medium

8. The variance measure of a variable, with values clustered more closely around the mean value, is larger than when the values are more widely dispersed from the mean.

Learning Objective: 10-1: Choose and interpret basic statistics to describe distribution of values of a single variable (univariate statistics).

Cognitive Domain: Comprehension

Answer Location: Variance

Difficulty Level: Medium

9. 99.7% of values fall within +/- 3 standard deviation from the mean of a normally distributed variable.

Learning Objective: 10-2: Assess plausibility of univariate statistical results.

Cognitive Domain: Knowledge

Answer Location: Plausibility Criteria for Univariate Statistics

Difficulty Level: Medium

10. The variance measure of a variable is in the same units as the variable values.

Learning Objective: 10-2: Assess plausibility of univariate statistical results.

Cognitive Domain: Knowledge

Answer Location: Plausibility Criteria for Univariate Statistics

Difficulty Level: Hard

Short Answer

1. What is the plausible value range of a measure of position such as percentiles? Explain your answer.

Learning Objective: 10-2: Assess plausibility of univariate statistical results.

Cognitive Domain: Knowledge

Answer Location: Plausibility Criteria for Univariate Statistics

Difficulty Level: Medium

2. Which is the best way to portray the distribution of a categorical variable? Explain with an example.

Learning Objective: 10-3: Design and read tables and charts to display distributions.

Cognitive Domain: Comprehension

Answer Location: Portraying distribution of categorical variables

Difficulty Level: Medium

3. With the help of an example, illustrate the best way to present data distribution of a nominal variable. Explain your reasons for such a presentation.

Learning Objective: 10-3: Design and read tables and charts to display distributions.

Cognitive Domain: Application

Answer Location: Nominal variables

Difficulty Level: Hard

4. The mean and median value of a continuous variable are 10.4 and 9.5 respectively. The maximum value of the variable is 41.7. How would these values be shown in a box-and-whiskers plot?

Learning Objective: 10-3: Design and read tables and charts to display distributions.

Cognitive Domain: Application

Answer Location: Portraying Distribution of Continuous Variables

Difficulty Level: Medium

5. What is a bivariate association? Explain, with an example, the measure(s) used to show this type of an association.

Learning Objective: 10-4: Select and interpret statistics to describe the relationship between two variables (bivariate statistics).

Cognitive Domain: Comprehension

Answer Location: Association Between Two or More Variable

Difficulty Level: Easy

6. Why is a numeric association between 2 variables, not necessarily indicative of a cause-effect relationship between the variables? Explain with an example.

Learning Objective: 10-4: Select and interpret statistics to describe the relationship between two variables (bivariate statistics).

Cognitive Domain: Comprehension

Answer Location: Association Between Two or More Variables

Difficulty Level: Hard

7. The correlation coefficient between two variables was found to be 0.37. What is the coefficient of determination between the two variables? What does this measure represent?

Learning Objective: 10-4: Select and interpret statistics to describe the relationship between two variables (bivariate statistics).

Cognitive Domain: Application

Answer Location: Correlation

Difficulty Level: Medium

8. When would you use ANOVA, rather than a difference in means, to measure association between a continuous and a categorical variable? Explain with an example.

Learning Objective: 10-4: Select and interpret statistics to describe the relationship between two variables (bivariate statistics).

Cognitive Domain: Comprehension

Answer Location: Difference in Means or ANOVA

Difficulty Level: Medium

9. What is the difference between ANOVA and a 2-way ANOVA. Illustrate with an example.

Learning Objective: 10-6: Identify methods used to describe associations among three variables.

Cognitive Domain: Comprehension

Answer Location: Two-way Difference In Means or 2-way ANOVA

Difficulty Level: Hard

10. What are the plausible limits on values of the coefficient of determination measure? How are these different from limits of the correlation coefficient measure?

Learning Objective: 10-7: Assess plausibility of bivariate and three-way results.

Cognitive Domain: Knowledge

Answer Location: Plausibility Criteria For Bivariate and Three-Way Statistics

Difficulty Level: Easy

Essay

1. Design a research study on a topic of your choice. Make sure the outcome is a continuous variable, and that there are at least three independent variables with one of them being categorical. Construct a table with the variables in columns, and each observation or case for those variables, in rows. Have between seven to 10 rows in the table. Insert artificial values in each cell corresponding to the variable value for each row. This will be your data used in the study. If you have or find any public data on the topic of your choice, you could use it as your data source. You could also use survey data collected by the Center for Disease Control (CDC) on smoking habits among youth. You could access this data at https://www.cdc.gov/tobacco/data_statistics/surveys/nyts/index.htm. Now, create a report showing central tendency, variability, and shape of any two of your variables in the study. Explain any calculations you make to arrive at your report results.

Learning Objective: 10-1: Choose and interpret basic statistics to describe distribution of values of a single variable (univariate statistics).

Cognitive Domain: Application

Answer Location: Distributions of Single Variables

Difficulty Level: Medium

2. For the research study in question 1, create a report giving measures and charts (where applicable) for a bivariate and a three-way association between the variables in the study.

Learning Objective: 10-4: Select and interpret statistics to describe the relationship between two variables (bivariate statistics).

Cognitive Domain: Application

Answer Location: Association Between Two or More Variables

Difficulty Level: Hard

3. Discuss the plausibility of values, and their limits, for the numbers you present in your reports in question 1 and 2. Explain your reasoning.

Learning Objective: 10-7: Assess plausibility of bivariate and three-way results.

Cognitive Domain: Application

Answer Location: Plausibility Criteria For Bivariate and Three-Way Statistics

Difficulty Level: Medium