Social Statistics For A Diverse Society 8th Edition By Frankfort Nachmias - Test Bank

Chapter 4: Measures of Variability Test Bank Multiple Choice 1. Numbers that describe diversity in a distribution are referred to as measures of a. central tendency. b. association. c. variability. d. standard deviation. Ans: c Learning Objective: 4-1: Explain the importance of measuring variability Cognitive Domain: Knowledge Answer Location: Measures of Variability Difficulty Level: Easy 2. Which measure of variability is used for nominal variables such as race and ethnicity? a. Mode b. Index of qualitative variation c. Standard deviation d. Stratified variance Ans: b Learning Objective: 4-2: Calculate and interpret the index of qualitative variation, range, interquartile range, the variance, and the standard deviation Cognitive Domain: Knowledge Answer Location: Index of Qualitative Variation Difficulty Level: Easy 3. How can an IQV of .35, which describes the level of racial diversity in a southern U.S. state, be interpreted? a. 35 respondents account for the total amount of variability in the state. b. 35 respondents do not account for the total amount of variability in the state. c. There is more variability for 35% of the respondents compared to the remaining 65%. d. The southern state of interest sees 35% of the maximum possible racial differences. Ans: d Learning Objective: 4-2: Calculate and interpret the index of qualitative variation, range, interquartile range, the variance, and the standard deviation Cognitive Domain: Comprehension Answer Location: Expressing IQV as a Percentage Difficulty Level: Easy 4. The quantity that is arrived at by taking the highest score minus the lowest score is referred to as the a. interquartile range. b. range. c. standard deviation. d. variance. Ans: b Learning Objective: 4-2: Calculate and interpret the index of qualitative variation, range, interquartile range, the variance, and the standard deviation Cognitive Domain: Knowledge Answer Location: The Range Difficulty Level: Easy 5. The width of the middle 50% of a distribution, defined as the difference between the third and first quartiles, is referred to as the a. interquartile range. b. range. c. standard deviation. d. variance. Ans: a Learning Objective: 4-2: Calculate and interpret the index of qualitative variation, range, interquartile range, the variance, and the standard deviation Answer Location: The Interquartile Range Cognitive Domain: Knowledge Difficulty Level: Easy 6. Consider the following hypothetical scores: 21, 25, 37, 38, 39, 42, 44, 45. What is the value of the range? a. 1 b. 5 c. 17 d. 24 Ans: d Learning Objective: 4-2: Calculate and interpret the index of qualitative variation, range, interquartile range, the variance, and the standard deviation Cognitive Domain: Application Answer Location: The Range Difficulty Level: Easy 7. Consider the following hypothetical scores: 21, 25, 37, 38, 39, 42, 44, 45. What is the value of the interquartile range? a. 1 b. 5 c. 17 d. 24 Ans: c Learning Objective: 4-2: Calculate and interpret the index of qualitative variation, range, interquartile range, the variance, and the standard deviation Cognitive Domain: Application Answer Location: The Interquartile Range Difficulty Level: Medium 8. Consider the following hypothetical scores: 21, 25, 37, 38, 39, 42, 44, 45. Which value is closest to the variance? a. 9 b. 19 c. 24 d. 77 Ans: d Learning Objective: 4-2: Calculate and interpret the index of qualitative variation, range, interquartile range, the variance, and the standard deviation Cognitive Domain: Application Answer Location: Calculating the Variance and the Standard Deviation Difficulty Level: Medium 9. Consider the following hypothetical scores: 21, 25, 37, 38, 39, 42, 44, 45. Which value is closest to the standard deviation? a. 9 b. 17 c. 24 d. 77 Ans: a Learning Objective: 4-2: Calculate and interpret the index of qualitative variation, range, interquartile range, the variance, and the standard deviation Cognitive Domain: Application Answer Location: Calculating the Variance and the Standard Deviation Difficulty Level: Medium 10. A graphic device that is able to simultaneously present the range, the interquartile range, the median, and the minimum and maximum scores is referred to as a a. box plot. b. the bar graph. c. the histogram. d. the line graph. Ans: a Learning Objective: 4-1: Explain the importance of measuring variability Cognitive Domain: Knowledge Answer Location: The Box Plot Difficulty Level: Easy 11. Which measure of variability is the average of the squared deviations from the mean and is used for interval-ratio variables? a. IQV b. Interquartile range c. Variance d. Standard deviation Ans: c Learning Objective: 4-2: Calculate and interpret the index of qualitative variation, range, interquartile range, the variance, and the standard deviation Cognitive Domain: Knowledge Answer Location: The Variance and the Standard Deviation Difficulty Level: Medium 12. Which measure of variability is used for interval-ratio variables and is the square root of the average of the squared deviations from the mean? a. IQV b. Interquartile range c. Variance d. Standard deviation Ans: d Learning Objective: 4-2: Calculate and interpret the index of qualitative variation, range, interquartile range, the variance, and the standard deviation Cognitive Domain: Knowledge Answer Location: The Variance and the Standard Deviation Difficulty Level: Medium 13. Which three quantities are needed to calculate the variance? a. Mean, median, and mode b. Mean, observed Y, N c. Median, observed Y, N d. Mean, standard deviation, N Ans: b Learning Objective: 4-2: Calculate and interpret the index of qualitative variation, range, interquartile range, the variance, and the standard deviation Cognitive Domain: Comprehension Answer Location: Calculating the Variance and the Standard Deviation Difficulty Level: Medium 14. Consider the variable, type of birth control practiced (e.g., an IUD, condoms, none, etc). Which measure of variability is best suited to describe variation in the distribution of this variable? a. IQV b. Range c. Variance d. Standard deviation Ans: a Learning Objective: 4-2: Calculate and interpret the index of qualitative variation, range, interquartile range, the variance, and the standard deviation Cognitive Domain: Analysis Answer Location: Index of Qualitative Variation Difficulty Level: Medium 15. Consider the following hypothetical scores: 21, 25, 37, 38, 39, 42, 44, 45. What is the closest value of the mean? a. 1 b. 5 c. 36 d. 24 Ans: c Learning Objective: 4-2: Calculate and interpret the index of qualitative variation, range, interquartile range, the variance, and the standard deviation Cognitive Domain: Application Answer Location: Calculating the Deviation from the Mean Difficulty Level: Easy 16. The type of information on how scores are spread from the center of a distribution is obtained by a. measures of central tendency. b. measures of variability. c. median. d. mean. Ans: b Learning Objective: 4-1: Explain the importance of measuring variability Cognitive Domain: Comprehension Answer Location: Measures of Variability Difficulty Level: Easy 17. The index of qualitative variation can vary from a. –1.00 to 0.00. b. 0.00 to 0.50. c. 0.00 to 1.00. d. –1.00 to 1.00. Ans: c Learning Objective: 4-2: Calculate and interpret the index of qualitative variation, range, interquartile range, the variance, and the standard deviation Cognitive Domain: Knowledge Answer Location: Index of Qualitative Variation Difficulty Level: Easy 18. The range is a measure of variability for a. only ordinal variables. b. ordinal variables. c. only interval-ratio variables. d. interval ratio variables. Ans: c Learning Objective: 4-2: Calculate and interpret the index of qualitative variation, range, interquartile range, the variance, and the standard deviation Cognitive Domain: Comprehension Answer Location: The Range Difficulty Level: Medium Multiple Response 1. SELECT ALL THAT APPLY. Consider the following hypothetical data: Catholic = 32, Protestant = 25, Jewish = 4, Muslim = 8, Other = 29, and None = 2. Which of the following statements are true? a. IQV = 0.89 b. IQV = 0.11 c. Number of religious difference is 89% of the maximum possible difference d. Number of religious difference is 11% of the maximum possible difference Ans: a, c Learning Objective: 4-2: Calculate and interpret the index of qualitative variation, range, interquartile range, the variance, and the standard deviation Cognitive Domain: Application Answer Location: Steps for Calculating IQV Difficulty Level: Medium 2. SELECT ALL THAT APPLY. The interquartile range is a measure of variability for a. only ordinal variables. b. ordinal variables. c. only interval-ratio variables. d. interval-ratio variables. Ans: b, d Learning Objective: 4-2: Calculate and interpret the index of qualitative variation, range, interquartile range, the variance, and the standard deviation Cognitive Domain: Comprehension Answer Location: The Interquartile Range Difficulty Level: Medium 3. SELECT ALL THAT APPLY. The formula for calculating interquartile range is a. Q3 – Q1. b. Q1 – Q3. c. 25th percentile – 75th percentile. d. 75th percentile – 25th percentile. Ans: a, d Learning Objective: 4-2: Calculate and interpret the index of qualitative variation, range, interquartile range, the variance, and the standard deviation Cognitive Domain: Knowledge Answer Location: The Interquartile Range Difficulty Level: Easy 4. SELECT ALL THAT APPLY. The box plot can visually present a. the range. b. the IQR. c. the median. d. the IQV. Ans: a, b, c Learning Objective: 4-1: Explain the importance of measuring variability Cognitive Domain: Knowledge Answer Location: The Box Plot Difficulty Level: Easy 5. SELECT ALL THAT APPLY. In a distribution where all the scores are identical, a. the standard deviation is zero. b. distribution is skewed. c. the variance is zero. d. the mean, median, and mode are all the same. Ans: a, c, d Learning Objective: 4-2: Calculate and interpret the index of qualitative variation, range, interquartile range, the variance, and the standard deviation Cognitive Domain: Comprehension Answer Location: Calculating the Variance and the Standard Deviation Difficulty Level: Medium True/False 1. IQV is based on the ratio of the total number of differences in the distribution to the maximum number of possible differences within the same distribution. Ans: T Learning Objective: 4-2: Calculate and interpret the index of qualitative variation, range, interquartile range, the variance, and the standard deviation Cognitive Domain: Knowledge Answer Location: Index of Qualitative Variation Difficulty Level: Easy 2. The quantities that are needed to calculate IQV are: the number of categories and the sum of all percentages in the distribution. Ans: F Learning Objective: 4-2: Calculate and interpret the index of qualitative variation, range, interquartile range, the variance, and the standard deviation Cognitive Domain: Knowledge Answer Location: Steps for Calculating the IQV Difficulty Level: Medium 3. The simplest and most straightforward measure of variation is the range. Ans: T Learning Objective: 4-2: Calculate and interpret the index of qualitative variation, range, interquartile range, the variance, and the standard deviation Cognitive Domain: Analysis Answer Location: The Range Difficulty Level: Easy 4. The range is based on only one score. Ans: F Learning Objective: 4-2: Calculate and interpret the index of qualitative variation, range, interquartile range, the variance, and the standard deviation Cognitive Domain: Knowledge Answer Location: The Range Difficulty Level: Easy 5. The box plot of a perfectly symmetrical distribution will have the box at the centre of the range as well as the median in the center of the box. Ans: T Learning Objective: 4-1: Explain the importance of measuring variability Cognitive Domain: Comprehension Answer Location: The Box Plot Difficulty Level: Easy 6. The variance is a measure of variation applicable only to ordinal variable. Ans: F Learning Objective: 4-2: Calculate and interpret the index of qualitative variation, range, interquartile range, the variance, and the standard deviation Cognitive Domain: Comprehension Answer Location: The Variance and the Standard Deviation Difficulty Level: Medium 7. The sum of the deviations of scores from the mean is always positive. Ans: F Learning Objective: 4-2: Calculate and interpret the index of qualitative variation, range, interquartile range, the variance, and the standard deviation Cognitive Domain: Comprehension Answer Location: Calculating the Deviation from the Mean Difficulty Level: Easy Short Answer 1. Suppose you are interested in examining the variability in current marital status by race. Which measure of variability would you use and why? Ans: The IQV because the variables are nominal. Learning Objective: 4-2: Calculate and interpret the index of qualitative variation, range, interquartile range, the variance, and the standard deviation Cognitive Domain: Analysis Answer Location: Index of Qualitative Variation Difficulty Level: Easy 2. Calculate the value of the appropriate measure of variability for each racial group. White Black Married 51.7% 27.3% Widowed 8.9% 8.5% Divorced 17.2% 16.1% Separated 2.5% 5.5% Never Married 19.7% 42.6% Ans: Whites = .82; Blacks = .88 Learning Objective: 4-2: Calculate and interpret the index of qualitative variation, range, interquartile range, the variance, and the standard deviation Cognitive Domain: Application Answer Location: Index of Qualitative Variation Difficulty Level: Medium 3. Calculate and provide a substantive interpretation of the value of the IQV. White Black Married 51.7% 27.3% Widowed 8.9% 8.5% Divorced 17.2% 16.1% Separated 2.5% 5.5% Never Married 19.7% 42.6% Ans: For whites, the number of marital status difference is about 82% of the maximum possible differences. For blacks, the number of marital status difference is about 88% of the maximum possible differences. Learning Objective: 4-2: Calculate and interpret the index of qualitative variation, range, interquartile range, the variance, and the standard deviation Cognitive Domain: Application Answer Location: Index of Qualitative Variation Difficulty Level: Medium 4. Calculate the value of the interquartile range for the following sub-sample: 2, 7, 4, 4, 1, 2, 2, 3, 1, 2, 4, 5. Ans: 2 Learning Objective: 4-2: Calculate and interpret the index of qualitative variation, range, interquartile range, the variance, and the standard deviation Cognitive Domain: Application Answer Location: The Interquartile Range Difficulty Level: Medium 5. Calculate the range for the following sub-sample: 2, 7, 4, 4, 1, 2, 2, 3, 1, 2, 4, 5. Ans: 6 Learning Objective: 4-2: Calculate and interpret the index of qualitative variation, range, interquartile range, the variance, and the standard deviation Cognitive Domain: Application Answer Location: The Range Difficulty Level: Easy 6. Calculate the values of the mean for the following sub-sample: 2, 7, 4, 4, 1, 2, 2, 3, 1, 2, 4, 5. Ans: Mean = 3.08 Learning Objective: 4-2: Calculate and interpret the index of qualitative variation, range, interquartile range, the variance, and the standard deviation Cognitive Domain: Application Answer Location: Calculating the Deviation from the Mean Difficulty Level: Easy 7. Construct a box plot based on the following sub-sample: 2, 7, 4, 4, 1, 2, 2, 3, 1, 2, 4, 5. Be sure to show the following quantities in your box plot: the minimum score, the maximum score, the range, interquartile range, and the median. Ans: Learning Objective: 4-1: Explain the importance of measuring variability Cognitive Domain: Application Answer Location: The Box Plot Difficulty Level: Medium 8. Calculate the value of the interquartile range for the following sub-sample: 24, 27, 35, 31, 21, 22, 28, 18, 25, 24, 36, 20. Ans: 7 Learning Objective: 4-2: Calculate and interpret the index of qualitative variation, range, interquartile range, the variance, and the standard deviation Cognitive Domain: Application Answer Location: The Interquartile Range Difficulty Level: Medium 9. Calculate the values of the mean for the following sub-sample: 24, 27, 35, 31, 21, 22, 28, 18, 25, 24, 36, 20. Ans: Mean = 25.92 Learning Objective: 4-2: Calculate and interpret the index of qualitative variation, range, interquartile range, the variance, and the standard deviation Cognitive Domain: Application Answer Location: Calculating the deviation from the Mean Difficulty Level: Easy 10. Calculate the range for the following sub-sample: 24, 27, 35, 31, 21, 22, 28, 18, 25, 24, 36, 20. Ans: 18 Learning Objective: 4-2: Calculate and interpret the index of qualitative variation, range, interquartile range, the variance, and the standard deviation Cognitive Domain: Application Answer Location: The Range Difficulty Level: Easy 11. Construct a box plot based on the following data: 24, 27, 35, 31, 21, 22, 28, 18, 25, 24, 36, 20. Be sure to show the following quantities in your box plot: the minimum score, the maximum score, the range, interquartile range, and the median. Ans: Learning Objective: 4-1: Explain the importance of measuring variability Cognitive Domain: Application Answer Location: The Box Plot Difficulty Level: Medium 12. What is the most basic consideration in choosing a measure of variability? Ans: The variable’s level of measurement. Learning Objective: 4-3: Identify the relative strengths and weaknesses of the measures Cognitive Domain: Analysis Answer Location: Considerations for Choosing a Measure of Variation Difficulty Level: Medium 13. What are the relative strengths and weaknesses of using range as a measure of variability? Ans: The strength of using range as a measure of variability is its easy calculation whereas its major weakness is that it uses only two points from all the scores and hence will not provide a good idea of the variation of the rest of the scores. Learning Objective: 4-3: Identify the relative strengths and weaknesses of the measures Cognitive Domain: Analysis Answer Location: The Range Difficulty Level: Easy 14. What are the relative strengths and weaknesses of using standard deviation as a measure of variability? Ans: The strength of using standard deviation as a measure of variability is it calculates the deviation of each score from the mean and hence uses all scores provided. The elaborate and time-consuming calculation is the major weakness of this method. Learning Objective: 4-3: Identify the relative strengths and weaknesses of the measures Cognitive Domain: Analysis Answer Location: The Variance and the Standard Deviation Difficulty Level: Medium Essay 1. Calculate the value of variance for the following sub-sample: 24, 27, 35, 31, 21, 22, 28, 18, 25, 24, 36, 20. Ans: 32.81 Learning Objective: 4-2: Calculate and interpret the index of qualitative variation, range, interquartile range, the variance, and the standard deviation Cognitive Domain: Application Answer Location: Calculating Variance and the Standard Deviation Difficulty Level: Medium 2. Calculate the value of the standard deviation for the following sub-sample: 24, 27, 35, 31, 21, 22, 28, 18, 25, 24, 36, 20. Ans: 5.73 Learning Objective: 4-2: Calculate and interpret the index of qualitative variation, range, interquartile range, the variance, and the standard deviation Cognitive Domain: Application Answer Location: Calculating Variance and the Standard Deviation Difficulty Level: Medium 3. Calculate the value of variance for the following sub-sample: 2, 7, 4, 4, 1, 2, 2, 3, 1, 2, 4, 5 Ans: 3.17 Learning Objective: 4-2: Calculate and interpret the index of qualitative variation, range, interquartile range, the variance, and the standard deviation Cognitive Domain: Application Answer Location: Calculating the Variance and the Standard Deviation Difficulty Level: Medium 4. Calculate the value of the standard deviation for the following sub-sample: 2, 7, 4, 4, 1, 2, 2, 3, 1, 2, 4, 5 Ans: 1.78 Learning Objective: 4-2: Calculate and interpret the index of qualitative variation, range, interquartile range, the variance, and the standard deviation Cognitive Domain: Application Answer Location: Calculating the Variance and the Standard Deviation Difficulty Level: Medium 5. Calculate the value of the variance for the following sub-sample: 3, 13, –4, 10, 0, 12, –1, –2, 6, 9, 5, 11 Ans: 36.54 Learning Objective: 4-2: Calculate and interpret the index of qualitative variation, range, interquartile range, the variance, and the standard deviation Cognitive Domain: Application Answer Location: Calculating the Variance and the Standard Deviation Difficulty Level: Medium 6. Calculate the value of the standard deviation for the following sub-sample: 3, 13, –4, 10, 0, 12, –1, –2, 6, 9, 5, 11. Ans: 6.04 Learning Objective: 4-2: Calculate and interpret the index of qualitative variation, range, interquartile range, the variance, and the standard deviation Cognitive Domain: Application Answer Location: Calculating the Variance and the Standard Deviation Difficulty Level: Medium Social Statistics 8th Edition Test Bank, Frankfort Nachmias Test Bank, Statistics Test Bank for Social Sciences, Test Bank for Diverse Society Statistics, Social Research Methods Test Bank, Quantitative Analysis Test Bank, Social Data Analysis Test Bank, Test Questions for Statistical Methods, Social Science Research Test Bank, Statistical Inference Test Bank, Descriptive Statistics Exam Questions, Inferential Statistics Test Bank, Probability and Sampling Test Bank, Hypothesis Testing Test Bank, Regression Analysis Exam Questions, Multivariate Statistics Test Bank, Test Bank for Research Design, Data Collection Techniques Exam Questions, Survey Research Methods Test Bank, Statistical Software Tools Test Bank, Data Analysis and Interpretation Test Bank, Test Bank for Social Science Surveys, 8th Edition Frankfort Nachmias Test Bank, Social Statistics Test Bank PDF, Social Statistics Test Bank Download, Diversity in Social Research Test Bank, Test Bank for Sociological Data Analysis, Applied Social Statistics Test Bank, Test Bank for Research Methods in Social Sciences, Social Research Design and Analysis Test Bank.