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Active Learning Lecture Slides For use with Classroom Response Systems Chapter 2: Exploring Data with Graphs and Numerical Summaries Statistics: The Art and Science of Learning from Data Second Edition by Agresti/Franklin 2.1.1) Identify the list which contains only categorical variables? a) month of birth, age, favorite color b) month of birth, height, weight c) marital status, major in school, HIV status d) marital status, height, favorite color e) HIV status, marital status, GPA Copyright © 2009 Pearson Education, Inc. 2.1.1) Identify the list which contains only categorical variables? a) month of birth, age, favorite color b) month of birth, height, weight c) marital status, major in school, HIV status d) marital status, height, favorite color e) HIV status, marital status, GPA Copyright © 2009 Pearson Education, Inc. 2.1.2) Identify the list which contains only quantitative variables. a) favorite food, height, SAT score b) weight, zip code, height c) GPA, height, SAT score d) time to run 15K, SAT score, HIV status e) time to run 15K, major in school, zip code Copyright © 2009 Pearson Education, Inc. 2.1.2) Identify the list which contains only quantitative variables. a) favorite food, height, SAT score b) weight, zip code, height c) GPA, height, SAT score d) time to run 15K, SAT score, HIV status e) time to run 15K, major in school, zip code Copyright © 2009 Pearson Education, Inc. 2.1.3) Identify the answer choice that is an example of a discrete quantitative variable. a) The number of people to complete a 5K run b) The time to complete a 5K run c) The weight of each participant in the 5K run d) The amount of donations received e) The type of running shoes worn in the 5K run Copyright © 2009 Pearson Education, Inc. 2.1.3) Identify the answer choice that is an example of a discrete quantitative variable. a) The number of people to complete a 5K run b) The time to complete a 5K run c) The weight of each participant in the 5K run d) The amount of donations received e) The type of running shoes worn in the 5K run Copyright © 2009 Pearson Education, Inc. 2.1.4) Identify the answer choice that is an example of a continuous quantitative variable. a) The year a car was manufactured. b) The country in which the car was manufactured. c) The number of cylinders the car has (4,6,8…) d) The time it takes the car to reach 60 mph from a dead stop. e) The color of the car. Copyright © 2009 Pearson Education, Inc. 2.1.4) Identify the answer choice that is an example of a continuous quantitative variable. a) The year a car was manufactured. b) The country in which the car was manufactured. c) The number of cylinders the car has (4,6,8…) d) The time it takes the car to reach 60 mph from a dead stop. e) The color of the car. Copyright © 2009 Pearson Education, Inc. 2.2.1) In 2006 the GSS asked, “How often do you read a traditional newspaper?” (i.e. one that is printed with ink on paper and NOT counting what you read online). The answers are displayed in the table below. What is the mode? a) Every Day b) A few times a week c) Once a week d) Less than once a week e) Never Copyright © 2009 Pearson Education, Inc. 2.2.1) In 2006 the GSS asked, “How often do you read a traditional newspaper?” (i.e. one that is printed with ink on paper and NOT counting what you read online). The answers are displayed in the table below. What is the mode? a) Every Day b) A few times a week c) Once a week d) Less than once a week e) Never Copyright © 2009 Pearson Education, Inc. 2.2.2) In 2002 the GSS asked, “How important is it for a person to be considered an adult for them to be no longer living in their parents’ household?”. The responses are listed in the table below. Approximately how many participants were asked this question? a) b) c) d) e) 5 500 1000 1300 1500 Copyright © 2009 Pearson Education, Inc. 2.2.2) In 2002 the GSS asked, “How important is it for a person to be considered an adult for them to be no longer living in their parents’ household?”. The responses are listed in the table below. Approximately how many participants were asked this question? a) b) c) d) e) 5 500 1000 1300 1500 Copyright © 2009 Pearson Education, Inc. 2.2.3) The amount of rainfall (in.) per day in July 2007 in Gainesville, Florida was recorded. A stem-and-leaf plot of the data was made in Minitab. What was the most rain received per day? a) b) c) d) e) 0.117 inches 0.17 inches 1.17 inches 1.7 inches 11.7 inches Stem-and-Leaf Display: Amount of Rainfall Stem-and-leaf of Amount of Rainfall N = 31 Leaf Unit = 0.10 (27) 0 000000000000000000000000111 4 0 22 2 0 4 1 0 1 0 1 1 1 1 1 1 1 1 7 Copyright © 2009 Pearson Education, Inc. 2.2.3) The amount of rainfall (in.) per day in July 2007 in Gainesville, Florida was recorded. A stem-and-leaf plot of the data was made in Minitab. What was the most rain received per day? a) b) c) d) e) 0.117 inches 0.17 inches 1.17 inches 1.7 inches 11.7 inches Stem-and-Leaf Display: Amount of Rainfall Stem-and-leaf of Amount of Rainfall N = 31 Leaf Unit = 0.10 (27) 0 000000000000000000000000111 4 0 22 2 0 4 1 0 1 0 1 1 1 1 1 1 1 1 7 Copyright © 2009 Pearson Education, Inc. 2.2.4) The amount of rainfall (in.) per day in July 2007 in Gainesville, Florida was recorded. A stem-and-leaf plot of the data was made in Minitab. What percentage of days was there over a half an inch of rain but less than one Stem-and-Leaf Display: Amount of Rainfall inch of rain? a) b) c) d) e) 0% 3.2% 3.3% 10% None of the above Stem-and-leaf of Amount of Rainfall N = 31 Leaf Unit = 0.10 (27) 0 000000000000000000000000111 4 0 22 2 0 4 1 0 1 0 1 1 1 1 1 1 1 1 7 Copyright © 2009 Pearson Education, Inc. 2.2.4) The amount of rainfall (in.) per day in July 2007 in Gainesville, Florida was recorded. A stem-and-leaf plot of the data was made in Minitab. What percentage of days was there over a half an inch of rain but less than one Stem-and-Leaf Display: Amount of Rainfall inch of rain? a) b) c) d) e) 0% 3.2% 3.3% 10% None of the above Stem-and-leaf of Amount of Rainfall N = 31 Leaf Unit = 0.10 (27) 0 000000000000000000000000111 4 0 22 2 0 4 1 0 1 0 1 1 1 1 1 1 1 1 7 Copyright © 2009 Pearson Education, Inc. 2.2.5) In 2005, the census bureau conducted a survey to determine the median income per household per state. What is the best description of the histogram of the results? a) b) c) d) Bi-modal Perfectly bell shaped Slightly left skewed Slightly right skewed Copyright © 2009 Pearson Education, Inc. 2.2.5) In 2005, the census bureau conducted a survey to determine the median income per household per state. What is the best description of the histogram of the results? a) b) c) d) Bi-modal Perfectly bell shaped Slightly left skewed Slightly right skewed Copyright © 2009 Pearson Education, Inc. 2.3.1) Which measure of center is most influenced by outliers? a) Mode b) Median c) Mean d) Standard deviation e) Variance Copyright © 2009 Pearson Education, Inc. 2.3.1) Which measure of center is most influenced by outliers? a) Mode b) Median c) Mean d) Standard deviation e) Variance Copyright © 2009 Pearson Education, Inc. 2.3.2) What can be said about the relationship between the mean and median in the dotplot below? a) The mean is smaller than the median. b) The mean is bigger than the median. c) The mean is equal to the median. d) Nothing can be determined based on the graph. Copyright © 2009 Pearson Education, Inc. 2.3.2) What can be said about the relationship between the mean and median in the dotplot below? a) The mean is smaller than the median. b) The mean is bigger than the median. c) The mean is equal to the median. d) Nothing can be determined based on the graph. Copyright © 2009 Pearson Education, Inc. 2.3.3) An investor was interested in determining how much gain she had in her 401K plan in the last 6 quarters. The data is listed below. Find the median and the mean of the data. -510 110 1230 1900 -680 1700 a) Mean = 1021.7 b) Mean = 1021.7 c) Mean = 625 d) Mean = 625 e) Mean = 625 Median = 670 Median = 1565 Median = 3.5 Median = 670 Median = 1565 Copyright © 2009 Pearson Education, Inc. 2.3.3) An investor was interested in determining how much gain she had in her 401K plan in the last 6 quarters. The data is listed below. Find the median and the mean of the data. -510 110 1230 1900 -680 1700 a) Mean = 1021.7 b) Mean = 1021.7 c) Mean = 625 d) Mean = 625 e) Mean = 625 Median = 670 Median = 1565 Median = 3.5 Median = 670 Median = 1565 Copyright © 2009 Pearson Education, Inc. 2.3.4) In 2004 one of the questions on the GSS survey asked respondents, "To how many service clubs do you belong?“. Find the median from the data listed in the table below. No. of Organizations Frequency 1 organization 111 2 organizations 14 a) 0 organizations 3 organizations b) 1 organization 4 organizations c) 2 organizations 7 or more organizations d) 3 organizations e) Cannot be determined Copyright © 2009 Pearson Education, Inc. 14 3 1 2.3.4) In 2004 one of the questions on the GSS survey asked respondents, "To how many service clubs do you belong?“. Find the median from the data listed in the table below. No. of Organizations Frequency 1 organization 111 2 organizations 14 a) 0 organizations 3 organizations b) 1 organization 4 organizations c) 2 organizations 7 or more organizations d) 3 organizations e) Cannot be determined Copyright © 2009 Pearson Education, Inc. 14 3 1 2.3.5) Find the median amount spent on a trip to the mall for 60 randomly selected residents of Atlanta, Georgia. Stem-and-leaf of money spent N = 60 Leaf Unit = 10 a) 45 dollars b) 46 dollars c) 47 dollars d) 450 dollars e) 470 dollars 1 2 5 4 3 003 15 3 55555556789 26 4 00000000012 (11) 4 55555577788 23 5 000022 17 5 55688 12 6 00000 7 6 5689 3 7 00 1 7 5 Copyright © 2009 Pearson Education, Inc. 2.3.5) Find the median amount spent on a trip to the mall for 60 randomly selected residents of Atlanta, Georgia. Stem-and-leaf of money spent N = 60 Leaf Unit = 10 a) 45 dollars b) 46 dollars c) 47 dollars d) 450 dollars e) 470 dollars 1 2 5 4 3 003 15 3 55555556789 26 4 00000000012 (11) 4 55555577788 23 5 000022 17 5 55688 12 6 00000 7 6 5689 3 7 00 1 7 5 Copyright © 2009 Pearson Education, Inc. 2.4.1) An investor was interested in determining how much gain she had in her 401K plan in the last 6 quarters. Find the range and the standard deviation from the data listed below. -510 110 1230 1900 -680 1700 a) b) c) d) Range = 2580 Range = 1220 Range = 2580 Range = 1220 Standard Deviation = 1131.7 Standard Deviation = 1131.7 Standard Deviation = 1033.1 Standard Deviation = 1033.1 Copyright © 2009 Pearson Education, Inc. 2.4.1) An investor was interested in determining how much gain she had in her 401K plan in the last 6 quarters. Find the range and the standard deviation from the data listed below. -510 110 1230 1900 -680 1700 a) b) c) d) Range = 2580 Range = 1220 Range = 2580 Range = 1220 Standard Deviation = 1131.7 Standard Deviation = 1131.7 Standard Deviation = 1033.1 Standard Deviation = 1033.1 Copyright © 2009 Pearson Education, Inc. 2.4.2) Which of the following is NOT a property of the standard deviation? a) It has the same units as the data. b) It can never be negative. c) It can be thought of as the average distance from the points to the mean. d) It can never equal zero. e) It is not resistant to outliers. Copyright © 2009 Pearson Education, Inc. 2.4.2) Which of the following is NOT a property of the standard deviation? a) It has the same units as the data. b) It can never be negative. c) It can be thought of as the average distance from the points to the mean. d) It can never equal zero. e) It is not resistant to outliers. Copyright © 2009 Pearson Education, Inc. 2.4.3) Suppose that the height of college males has a bell shaped distribution with a mean of 70 inches and a standard deviation of 2 inches. Approximately what percentage of college males are between 66 and 74 inches? a) 68% b) 90% c) 95% d) 99.7% e) 100% Copyright © 2009 Pearson Education, Inc. 2.4.3) Suppose that the height of college males has a bell shaped distribution with a mean of 70 inches and a standard deviation of 2 inches. Approximately what percentage of college males are between 66 and 74 inches? a) 68% b) 90% c) 95% d) 99.7% e) 100% Copyright © 2009 Pearson Education, Inc. 2.4.4) Which data set below would have a larger standard deviation? a) Data Set A b) Data Set B c) Data Set C d) The standard deviation is the same for all three data sets. e) Cannot be determined Copyright © 2009 Pearson Education, Inc. 2.4.4) Which data set below would have a larger standard deviation? a) Data Set A b) Data Set B c) Data Set C d) The standard deviation is the same for all three data sets. e) Cannot be determined Copyright © 2009 Pearson Education, Inc. 2.4.5) Suppose that the average salary for a K-12 teacher in South Carolina is $40,000. Which of the following values would be a reasonable value for the standard deviation? a) -1,000 b) 0 c) 1,000 d) 5,000 e) 13,000 Copyright © 2009 Pearson Education, Inc. 2.4.5) Suppose that the average salary for a K-12 teacher in South Carolina is $40,000. Which of the following values would be a reasonable value for the standard deviation? a) -1,000 b) 0 c) 1,000 d) 5,000 e) 13,000 Copyright © 2009 Pearson Education, Inc. 2.5.1) There are 13 students in an Introduction to Statistics class. Find the first and third quartiles of the scores for the class listed below. 60 65 65 70 75 75 75 80 80 80 85 85 85 a) b) c) d) e) Q1 = 65 Q1 = 70 Q1 = 67.5 Q1 = 65 Q1 = 70 Q3 = 80 Q3 = 85 Q3 = 82.5 Q3 = 82.5 Q3 = 80 Copyright © 2009 Pearson Education, Inc. 2.5.1) There are 13 students in an Introduction to Statistics class. Find the first and third quartiles of the scores for the class listed below. 60 65 65 70 75 75 75 80 80 80 85 85 85 a) b) c) d) e) Q1 = 65 Q1 = 70 Q1 = 67.5 Q1 = 65 Q1 = 70 Q3 = 80 Q3 = 85 Q3 = 82.5 Q3 = 82.5 Q3 = 80 Copyright © 2009 Pearson Education, Inc. 2.5.2) In Arizona the median salary for high school academic advisors is about $35,000. Use the data below to find the IQR for the salaries of Arizona high school academic advisors. x 34,000; s 4,000; Q1 29,000; Q3 38,000 a) b) c) d) IQR = $9,000 IQR = $6,000 IQR = $4,000 IQR = $3,000 Copyright © 2009 Pearson Education, Inc. 2.5.2) In Arizona the median salary for high school academic advisors is about $35,000. Use the data below to find the IQR for the salaries of Arizona high school academic advisors. x 34,000; s 4,000; Q1 29,000; Q3 38,000 a) b) c) d) IQR = $9,000 IQR = $6,000 IQR = $4,000 IQR = $3,000 Copyright © 2009 Pearson Education, Inc. 2.5.3) Below are some descriptive statistics about the median household income per state. Is Puerto Rico, with $20,107 dollars as its median income, a potential outlier? x 55, 062 a) Yes, it is below Q1-1.5*IQR. b) No, it is not below Q1 -1.5*IQR. c) Yes, it is the minimum so it is an outlier. d) It cannot be determined from the given information. s 9899 min 20107 Q1 48916 Q3 61401 max 75541 http://www.census.gov/hhes/www/income/statemedfaminc.html Copyright © 2009 Pearson Education, Inc. 2.5.3) Below are some descriptive statistics about the median household income per state. Is Puerto Rico, with $20,107 dollars as its median income, a potential outlier? x 55, 062 a) Yes, it is below Q1-1.5*IQR. b) No, it is not below Q1 -1.5*IQR. c) Yes, it is the minimum so it is an outlier. d) It cannot be determined from the given information. s 9899 min 20107 Q1 48916 Q3 61401 max 75541 http://www.census.gov/hhes/www/income/statemedfaminc.html Copyright © 2009 Pearson Education, Inc. 2.5.4) A personal trainer was interested in studying the effects of different types of diets (liquid diet, prepared meals, and low carb) on total weight loss in two months. What description below best describes the boxplots below? a) The range of the data sets are very similar. b) The median weight loss is similar for the diets. c) The third quartiles weight loss is similar for the diets. Copyright © 2009 Pearson Education, Inc. 2.5.4) A personal trainer was interested in studying the effects of different types of diets (liquid diet, prepared meals, and low carb) on total weight loss in two months. What description below best describes the boxplots below? a) The range of the data sets are very similar. b) The median weight loss is similar for the diets. c) The third quartiles weight loss is similar for the diets. Copyright © 2009 Pearson Education, Inc. 2.5.5) A personal trainer was interested in studying the effects of different types of diets (liquid diet, prepared meals, and low carb) on total weight loss in two months. Which boxplot has the biggest IQR? a) b) c) d) Liquid Diet Prepared Meals Low Carb They are the same e) Cannot be determined Copyright © 2009 Pearson Education, Inc. 2.5.5) A personal trainer was interested in studying the effects of different types of diets (liquid diet, prepared meals, and low carb) on total weight loss in two months. Which boxplot has the biggest IQR? a) b) c) d) Liquid Diet Prepared Meals Low Carb They are the same e) Cannot be determined Copyright © 2009 Pearson Education, Inc. 2.6.1) True or Not Always True: If given a choice between a straight bar graph and a bar graph with small figures, figures should be used because it makes it more interesting. a) True, graphs that use figures are more interesting so they have a greater impact on the audience. b) Not Always True, great care should be taken to make sure that the areas represented in the graph correspond accurately to the relative proportions. Copyright © 2009 Pearson Education, Inc. 2.6.1) True or Not Always True: If given a choice between a straight bar graph and a bar graph with small figures, figures should be used because it makes it more interesting. a) True, graphs that use figures are more interesting so they have a greater impact on the audience. b) Not Always True, great care should be taken to make sure that the areas represented in the graph correspond accurately to the relative proportions. Copyright © 2009 Pearson Education, Inc. 2.6.2) In general, when drawing graphs the vertical axis should start with ________. a) b) c) d) zero the minimum count for the smallest category a number ending in “0” an even number Copyright © 2009 Pearson Education, Inc. 2.6.2) In general, when drawing graphs the vertical axis should start with ________. a) b) c) d) zero the minimum count for the smallest category a number ending in “0” an even number Copyright © 2009 Pearson Education, Inc. 2.6.3) What can be done when you want to compare two groups of data but the groups have quite different values? a) Plot the two groups on separate graphs. b) Plot ratios using the data from the two groups on a single graph. c) Plot percentages using the data from the two groups on a single graph. d) All of the above. e) None of the above. Copyright © 2009 Pearson Education, Inc. 2.6.3) What can be done when you want to compare two groups of data but the groups have quite different values? a) Plot the two groups on separate graphs. b) Plot ratios using the data from the two groups on a single graph. c) Plot percentages using the data from the two groups on a single graph. d) All of the above. e) None of the above. Copyright © 2009 Pearson Education, Inc.