Seeing Through Statistics 4th Edition by Utts - Test Bank

CHAPTER 3 MEASUREMENTS, MISTAKES, AND MISUNDERSTANDINGS SECTION 3.1 SIMPLE MEASURES DON’T EXIST FREE RESPONSE QUESTIONS 1. Explain why even the simplest kind of measurement, such as finding your height, still presents complicated issues. ANSWER: ANY REASONABLE ANSWER OK. EXAMPLES: THE ACCURACY OF YOUR MEASUREMENT DEPENDS ON YOUR MEASUREMENT TOOL; HOW TALL YOU STAND WHEN YOU MEASURE; WHETHER OR NOT YOU WEAR SHOES, ETC. 2. Describe one of the issues that you would need to think about when deciding how to measure which supermarket is the ‘best’ one in town. ANSWER: ANY REASONABLE ANSWER OK. EXAMPLES: WHAT DO WE MEAN BY ‘BEST’? WHAT ONE PERSON THINKS OF AS ‘BEST’ MIGHT NOT MEAN THE SAME THING TO SOMEONE ELSE; DO WE MEASURE IT OVER TIME, OR AT ONE MOMENT IN TIME? MULTIPLE CHOICE QUESTIONS 3. What can happen if you don’t define your measurement properly? a. Your data could contain bias. b. Your data could be inaccurate and inconsistent. c. Your results could be questioned in a court of law. d. All of the above. ANSWER: D 4. Which of the following are examples of measurements? a. The gender of each member of your statistics class. b. Your opinion on whether smoking should be banned in all public places (support, oppose, no opinion). c. The number of deaths in each state in a given year due to accidents. d. All of the above. ANSWER: D SECTION 3.2 IT’S ALL IN THE WORDING FREE RESPONSE QUESTIONS 5. Political pollsters, who are only interested in surveying people who will actually vote, learned long ago that to determine whether or not someone is a likely voter, it is useless to simply ask them if they plan to vote. Explain why. ANSWER: MOST PEOPLE WILL SAY YES, CREATING BIAS IN THE SUBSEQUENT SURVEY RESULTS. 6. Explain why the ordering of questions on a survey can create bias in the resulting data. ANSWER: IF ONE QUESTION REQUIRES RESPONDENTS TO THINK ABOUT SOMETHING THAT THEY MAY NOT HAVE OTHERWISE CONSIDERED, THEN THE ORDER IN WHICH QUESTIONS ARE PRESENTED CAN CHANGE THE RESULTS. 7. Explain the difference between confidentiality and anonymity in a survey situation. ANSWER: IF THE SURVEY IS CONFIDENTIAL, THE RESEARCHER CAN ATTACH YOUR NAME TO YOUR RESULTS, BUT PROMISES NOT TO. IF THE SURVEY IS ANONYMOUS, THE RESEARCHER CANNOT ATTACH YOUR NAME TO YOUR RESULTS. 8. Name two of the pitfalls listed in your textbook that you have to watch out for when asking questions in a survey or experiment. ANSWER: ANY TWO OF THE FOLLOWING: 1) DELIBERATE BIAS; 2) UNINTENTIONAL BIAS; 3) DESIRE TO PLEASE; 4) ASKING THE UNINFORMED; 5) UNNECESSARY COMPLEXITY; 6) ORDERING OF QUESTIONS; OR 7) CONFIDENTIALITY VS. ANONYMITY. MULTIPLE CHOICE QUESTIONS 9. How much can respondents’ answers to survey questions change based on simple changes in wording? a. They won’t change much at all; changes in wording have little impact on the data. b. Answers can change a great deal, even with small changes in wording. c. The wording would have to change in a major way, but if it did, the answers would change as well. d. None of the above. ANSWER: B 10. Which of the following is not one of the pitfalls that can cause problems when asking questions in a survey or experiment? a. Deliberate bias b. Desire to please c. Ordering of questions d. All of the above are pitfalls ANSWER: D 11. A survey question that starts out with the phrase “Do you agree that...” is an example of what? a. Deliberate bias b. Unintentional bias c. Response bias d. Convenience bias ANSWER: A 12. What motivates a respondent to understate the true response about an undesirable social habit such as smoking? a. Wanting to create deliberate bias b. Desire to please c. Lack of memory d. None of the above ANSWER: B FILL-IN-THE-BLANK QUESTIONS 13. If a survey is __________ then the researcher cannot possibly attach your name to your survey results. ANSWER: ANONYMOUS 14. If a survey is __________ then the researcher can attach your name to your survey results, but promises not to release that information. ANSWER: CONFIDENTIAL SECTION 3.3 OPEN OR CLOSED QUESTIONS: SHOULD CHOICES BE GIVEN? FREE RESPONSE QUESTIONS 15. Suppose you want to set up a survey involving only closed questions. Why is it important to first conduct a pilot survey involving open questions? ANSWER: IF YOU DON’T OFFER THE MOST POPULAR POSSIBLE ANSWERS TO YOUR CLOSED QUESTION, EVEN IF YOU INCLUDE AN ALTERNATIVE OF ‘OTHER’, THE RESULTS OF YOUR SURVEY COULD CHANGE DRAMATICALLY, COMPARED TO THE RESULTS OF A SURVEY WITH ONLY OPEN QUESTIONS. 16. Name one of the major problems with offering open questions on a survey. ANSWER: THE BIGGEST PROBLEM WITH OPEN QUESTIONS IS THAT THE RESULTS CAN BE DIFFICULT TO SUMMARIZE, CATEGORIZE, OR QUANTIFY. 17. Explain why it is important as a consumer of statistical information to find out whether the questions on a survey or experiment were asked in an open or closed form. ANSWER: THIS IS IMPORTANT IN TERMS OF HOW YOU INTERPRET THE RESULTS, AND WHETHER OR NOT TO GIVE CREDIBILITY TO THE RESULTS. 18. Suppose you designed a survey with only closed questions, and for each question you included ‘other’ as one of the possible answers. Suppose for one of the questions you found that 75% of the respondents chose ‘other’. Explain why this is not a good thing, and what could have been done to prevent it. ANSWER: THIS IS NOT GOOD BECAUSE THE MOST POPULAR CHOICES WERE NOT OFFERED ON THE SURVEY, AND YOU LOST INFORMATION REGARDING WHAT THOSE CHOICES SHOULD HAVE BEEN. TO PREVENT THIS, CONDUCT A PILOT STUDY BEFOREHAND IN OPEN QUESTION FORM, AND INCLUDE THE MOST POPULAR ANSWERS AS CHOICES ON THE FINAL (CLOSED) VERSION OF THE QUESTION. MULTIPLE CHOICE QUESTIONS 19. What is the biggest problem with having open questions on a survey or in an experiment? a. The participants’ responses are difficult to summarize or categorize. b. You have to worry more about how an open question is worded than how a closed question is worded. c. There is no problem with open questions; they provide the most accurate information about how a person really feels. d. None of the above. ANSWER: A 20. What is the biggest problem with having closed questions on a survey or in an experiment? a. The choice of possible answers is critical and if not done properly, can lead to misleading information. b. The participants’ responses are hard to categorize or summarize. c. There is no problem with closed questions; they provide the most accurate information by offering certain explicit choices. d. You have to worry more about how a closed question is worded than how an open question is worded. ANSWER: A 21. Which of the following is an example of an open question? a. “Which of the following four issues do you feel is the most important problem facing this country today? If you prefer, you may name a different problem as most important; simply choose ‘other’ and explain your answer.” (Four choices are given, plus ‘other’.) b. “Don’t you think it’s time that we faced the fact that unemployment is the biggest problem facing this country today?” (Choices are: yes, no, no opinion.) c. “What do you feel is the most important problem facing this country today?” (No choices offered; participant must fill in the blank.) d. None of the above. ANSWER: C 22. Which of the following is an example of a closed question? a. “Which of the following four issues do you feel is the most important problem facing this country today? If you prefer, you may name a different problem as most important; simply choose ‘other’ and explain your answer.” (Four choices are given, plus ‘other’.) b. “Write down in one or two sentences how you feel about this statement: The biggest problem facing our nation today is a lack of presidential leadership.” c. “What do you feel is the most important problem facing this country today?” (No choices offered; participant must fill in the blank.) d. None of the above. ANSWER: A FILL-IN-THE-BLANK QUESTIONS 23. A (an) __________ question is one in which respondents are allowed to answer in their own words. ANSWER: OPEN 24. A (an) __________question is one in which the respondents are given a list of alternatives from which to choose their answer. ANSWER: CLOSED SECTION 3.4 DEFINING WHAT IS BEING MEASURED FREE RESPONSE QUESTIONS 25. When you read about measurements taken by someone else, you should not assume that they are measuring things the same way you think they should be measured. Give an example from the media where this problem might come up. ANSWER: RESEARCHERS MEASURE THINGS DIFFERENTLY; SOME DO A BETTER JOB THAN OTHERS. MEASUREMENTS THAT ARE INAPPROPRIATE OR INACCURATE CAN LEAD TO MISLEADING RESULTS. FOR EXAMPLE, IN ESTIMATING THE PERCENTAGE OF ‘HUNGRY’ CHILDREN, A SURVEY ASKED CHILDREN IF THEY HAD EVER BEEN HUNGRY. WHO WOULD SAY NO TO THAT? 26. Why do IQ tests continue to be surrounded by controversy as a measure of intelligence? ANSWER: IT IS VERY DIFFICULT TO DEFINE WHAT IS MEANT BY INTELLIGENCE. IT IS DIFFICULT TO MEASURE SOMETHING IF YOU CAN’T EVEN AGREE ON WHAT IT IS YOU ARE TRYING TO MEASURE. 27. Explain why it is so difficult to measure the amount of stress in someone’s life from a statistical standpoint. ANSWER: THERE IS NO FIXED DEFINITION OF STRESS. STRESS IS ALSO A RELATIVE MEASURE; WHAT IS HIGH STRESS TO ONE PERSON IS LOW OR MODERATE STRESS TO ANOTHER. 28. What is important for you to do as a good consumer of statistical information, when examining studies involving hard to measure items such as stress, happiness, or hunger? ANSWER: MAKE SURE YOU ARE INFORMED ABOUT HOW THE RESEARCHERS MEASURED THE ITEM, AND WHETHER THEIR METHODS WERE APPROPRIATE, CONSISTENT, AND ACCURATE. MULTIPLE CHOICE QUESTIONS 29. How can a measurement lead to misleading results in a survey? a. If the measurement leaves out obvious other possible choices. b. If the ‘no opinion’ or ‘neutral’ results are combined with either the positive or negative results to make that group appear larger than it really is. c. If the questions are worded in a misleading way. d. All of the above. ANSWER: D 30. What is the most common method for trying to measure attitudes and emotions? a. Have respondents read certain statements and determine the extent to which they agree/disagree with the statements. b. Use totally open ended questions in a face to face interview. c. Have participants evaluated by a psychotherapist. d. None of the above. ANSWER: A 31. How important is the wording of the question in terms of getting a good measurement in a survey or experiment? a. Extremely important. Poorly worded questions can lead to bias and inaccuracy. b. Only somewhat important; it’s the essence of the issue that matters. c. It shouldn’t matter at all. A question is a question. d. It depends on the situation. ANSWER: A 32. The U.S. Government regularly reports the unemployment rate. Which of the following is included in the U.S. government’s definition of what it means for a person to be unemployed? a. They don’t have a job. b. They have been actively looking for work in the prior four weeks. c. They are currently available for work. d. All of the above are included in the definition. ANSWER: D FILL-IN-THE-BLANK QUESTIONS 33. A good measurement has to be well __________ in order to give accurate and reliable data. ANSWER: DEFINED 34. When reading about a statistical study involving the amount of stress in a person’s life, be sure to find out exactly how stress was __________ by the researchers before deciding whether or not these results are credible. ANSWER: MEASURED OR DEFINED SECTION 3.5 DEFINING A COMMON LANGUAGE FREE RESPONSE QUESTIONS 35. Give an example of a measurement that is reliable but not valid. ANSWER: ONE WHICH GIVES REPEATABLE RESULTS BUT IS NOT AN APPROPRIATE MEASURE. EXAMPLE: USING A VERY PRECISE BATHROOM SCALE TO MEASURE PERCENTAGE OF BODY FAT. 36. What is measurement error? ANSWER: THE AMOUNT BY WHICH A MEASUREMENT DIFFERS FROM THE TRUE VALUE. 37. Explain the following statement: “The more variability there is within each group, the more difficult it is to detect a difference between groups.” ANSWER: SUPPOSE YOU WERE COMPARING MEN’S HEIGHTS TO WOMEN’S HEIGHTS. IF ALL THE MEN WERE THE SAME HEIGHT, AND ALL THE WOMEN WERE THE SAME HEIGHT, THE ONLY DIFFERENCE IN HEIGHT WOULD BE DUE TO GENDER. BUT BECAUSE OF NATURAL VARIABILITY FROM MAN TO MAN, AND FROM WOMAN TO WOMAN, THIS MAKES IT HARDER TO CLEARLY SEE DIFFERENCES IN HEIGHT BETWEEN MEN AND WOMEN. 38. Give three reasons why variability across measurements can occur. ANSWER: 1) MEASUREMENT ERROR; 2) NATURAL VARIABILITY ACROSS INDIVIDUALS AT ANY GIVEN TIME; AND 3) NATURAL VARIABILITY IN A CHARACTERISTIC OF THE SAME INDIVIDUAL ACROSS TIME. MULTIPLE CHOICE QUESTIONS 39. Which of the following is not an example of a discrete variable? a. The number of coins in a person’s pocket right now. b. Your exact age. c. The number of heads that could appear on two flips of a fair coin. d. All of the above are examples of a discrete variable. ANSWER: B 40. If you tried to measure happiness by using an IQ test, which of the following aspects of a good measurement would you be violating? a. V alidity b. Reliability c. Unbiasedness d. None of the above. ANSWER: A 41. If you used a 12-inch ruler to measure the distance across a large pond, which of the following aspects of a good measurement would you be violating? a. V alidity b. Reliability c. Unbiasedness d. None of the above. ANSWER: B 42. If you weighed yourself using a bathroom scale that always reads five pounds under the actual weight, which of the following aspects of a good measurement would you be violating? a. V alidity b. Reliability c. Unbiasedness d. None of the above. ANSWER: C FILL-IN-THE-BLANK QUESTIONS 43. __________ variables are those for which each individual can be placed into a group but the groups may not have any logical ordering. ANSWER: CATEGORICAL 44. __________ variables are those for which we can record a numerical value and then order the respondents according to those values. ANSWER: MEASUREMENT OR QUANTITATIVE CHAPTER 7 SUMMARIZING AND DISPLAYING MEASUREMENT DATA SECTION 7.1 TURNING DATA INTO INFORMATION FREE RESPONSE QUESTIONS 1. Name the four kinds of useful information that you can get about a set of measurement data once it has been organized and summarized. ANSWER: 1) THE CENTER; 2) THE VARIABILITY; 3) THE SHAPE; AND 4) UNUSUAL VALUES (OUTLIERS). For Questions 2-3, use the following narrative Narrative: Quiz scores Bob has taken 6 quizzes so far in his statistics class. Each quiz has a possible of 10 total points. Bob’s scores are the following: 10, 8, 9, 7, 2, and 9. 2. {Quiz scores narrative} Find the three measures of center for Bob’s quiz scores. ANSWER: THE MEAN (AVERAGE) IS 7.5; THE MODE IS 9; THE MEDIAN IS 8.5. 3. {Quiz scores narrative} Explain how (if) Bob’s lowest quiz score affects the mean and the median of this data set. ANSWER: THE 2 BRINGS DOWN THE MEAN (AVERAGE); IT DOES NOT AFFECT THE MEDIAN. 4. Name two questions that can be answered by determining the shape of a data set. ANSWER: ANY REASONABLE ANSWERS OK. EXAMPLES: 1) ARE MOST OF THE VALUES CLUMPED IN THE MIDDLE? ARE THERE TWO DISTINCT GROUPINGS? HOW MANY HIGH AND LOW VALUES ARE THERE, COMPARED TO THE NUMBER OF VALUES IN THE MIDDLE? MULTIPLE CHOICE QUESTIONS 5. Which of the following measures of center is affected by an outlier? a. Mean b. Median c. Mode d. All of the above ANSWER: A 6. The mode is most meaningful for which type of data? a. Measurement data b. Categorical data c. Biased data d. None of the above ANSWER: B 7. The amount of spread in the data is a measure of what characteristic of a data set? a. Center b. V ariability c. Shape d. None of the above ANSWER: B 8. What is the simplest measure of variability in a data set? a. The interquartile spread b. The outliers c. The range d. The standard deviation ANSWER: C FILL-IN-THE-BLANK QUESTIONS 9. The __________ is a measure of center with half of the scores falling at or above it and half of the scores falling at or below it. ANSWER: MEDIAN 10. One or two scores that are far removed from the rest of the data are called __________. ANSWER: OUTLIERS SECTION 7.2 PICTURING DATA: STEMPLOTS AND HISTOGRAMS For Questions 11-14, use the following narrative Narrative: School costs Suppose a random sample of liberal arts schools was taken, and the average cost per student was measured for each school. The data are pictured in the histogram below: FREE RESPONSE QUESTIONS 11. {School cost narrative} What is the shape of this data set? ANSWER: SKEWED TO THE RIGHT. DATA ALSO HAS AN OUTLIER ON THE HIGH END. 12. {School cost narrative} How many schools were sampled in this study? ANSWER: 25 13. {School cost narrative} Two measures of center were calculated for this data set and were found to be $26,668, and $34,832. One of them is the mean, and the other is the median. Which one is which, and how do you know that? ANSWER: $26,668 IS THE MEDIAN AND $34,832 IS THE MEAN. WHY: THE DATA IS SKEWED TO THE RIGHT AND HAS AN OUTLIER, BOTH OF WHICH DRIVE UP THE MEAN AND LEAVE THE MEDIAN UNAFFECTED. 14. {School cost narrative} Describe the four important characteristics of this data set (for example, the shape) using words that a parent exploring the cost of liberal arts colleges would find useful. ANSWER: CENTER: THE AVERAGE COST IS $34,832 PER STUDENT PER YEAR, AND THE MEDIAN COST IS $26,668 PER STUDENT PER YEAR; VARIABILITY: MOST OF THE SCHOOLS COST BETWEEN $15,000 AND $75,000 PER YEAR PER STUDENT; SHAPE: THE DATA ARE SKEWED TO THE RIGHT, MEANING THERE IS MORE VARIABILITY IN COST FOR SCHOOLS THAT ARE PRICIER; OUTLIERS: ONE SCHOOL IS AN OUTLIER, COSTING OVER $100,000 PER YEAR PER STUDENT. MULTIPLE CHOICE QUESTIONS 15. Which of the following pictures of a data set allows you to retrieve the actual data (assuming no digits are dropped)? a. A histogram b. A stemplot c. Both a) and b) d. Neither a) nor b) ANSWER: B 16. If the bars of a histogram represent the proportion of the total count that falls into each interval, what must the heights of the bars sum to? a. The total number of numbers in the data set. b. One. c. 1 divided by the total number of intervals used in the histogram. d. Not enough information to tell. ANSWER: B 17. Which of the following statements is true? a. If a data set is skewed to the right, that means there is bias in the results; the data are higher than they should be. b. If a data set is skewed to the right, then the higher values are more spread out than the lower values. c. If a data set is skewed to the right, then the lower values are more spread out than the higher values. d. None of the above. ANSWER: B 18. Which of the following statements regarding stemplots is false? a. A stemplot allows you to retrieve the original data (assuming no digits are dropped). b. A stemplot can never reuse the same stem digit twice. c. If a certain value in your data set is repeated three times, it must appear 3 times in appropriate stem and leaf of the stemplot. d. None of the above statements are false. ANSWER: B FILL-IN-THE-BLANK QUESTIONS 19. A __________ is a quick and easy way to put a list of numbers into order while getting a picture of their shape. ANSWER: STEMPLOT 20. A data set is __________ if the two halves of the data set (when cut down the middle) are mirror images of each other. ANSWER: SYMMETRIC SECTION 7.3 FIVE USEFUL NUMBERS: A SUMMARY FREE RESPONSE QUESTIONS 21. What are the five numbers used in a five-number summary? ANSWER: THE LOWEST (MINIMUM); THE HIGHEST (MAXIMUM); THE MEDIAN; THE LOWER QUARTILE; AND THE UPPER QUARTILE. For Questions 22-24, use the following narrative Narrative: Acceptance rates A random sample of 50 colleges and universities in the U.S. was selected, and acceptance rates were recorded for each school (percentage of student applicants who were accepted to the school). The following five-number summary was calculated for this data set: lowest = 17; lower quartile = 25.75; median = 36; upper quartile = 47.75; highest = 67. 22. {Acceptance rates narrative} Describe the shape of this data based on the five-number summary. ANSWER: THE DATA SET LOOKS FAIRLY EVENLY DISTRIBUTED EXCEPT FOR THE LAST QUARTER OF THE DATA, WHICH IS MORE SPREAD OUT THAN THE REST, INDICATING SKEWNESS TO THE RIGHT. 23. {Acceptance rates narrative} Describe the center of this data set in words a prospective student would understand. ANSWER: THE MEDIAN (MIDDLE) OF THE ACCEPTANCE RATES IS 36%. ABOUT HALF OF THE SCHOOLS ACCEPT 36% OR MORE OF APPLICANTS, AND ABOUT HALF ACCEPT 36% OR LESS. 24. {Acceptance rates narrative} Find the range of the acceptance rates and give one possible reason that it is such a high number. ANSWER: RANGE = 50; EXPLANATION: ANY REASONABLE ANSWER OK. EXAMPLES: AN OUTLIER WOULD AFFECT THE RANGE; THERE ARE MANY VARIABLES AFFECTING ACCEPTANCE RATES, INCLUDING TYPE OF INSTITUTION (LIBERAL ARTS VS. FOUR-YEAR UNIVERSITY, ETC); REGION OF THE U.S.; QUALITY OF EDUCATION; ETC. MULTIPLE CHOICE QUESTIONS 25. Suppose that in a five-number summary you find that a larger gap exists between the third quartile and the highest value than between the lowest value and the first quartile. What does this mean about the shape of the data set? a. Symmetric b. Skewed right c. Skewed left d. Not enough information to tell. ANSWER: B 26. Suppose that in a five-number summary you find that a larger gap exists between the extremes and the quartiles than between the quartiles and the median. What does this mean about the shape of the data set? a. The data are clumped at the high and low ends. b. The data are clumped in the middle. c. The data are not symmetric. d. Not enough information to tell. ANSWER: B 27. Which of the following does not require the data to be ordered before you can get the right answer? a. Mean b. Median c. Quartiles d. Range e. All of the above require the data to be ordered. ANSWER: A 28. Which a. Mean of the following is not included in the five-number summary? b. Median c. Lower quartile d. Highest number e. All of the above are included in the five-number summary. ANSWER: A FILL-IN-THE-BLANK QUESTIONS 29. The __________ are the medians of the two halves of an ordered data set. ANSWER: QUARTILES 30. A five-number summary involves the lower quartile, the upper quartile, the lowest number, the highest number, and the __________. ANSWER: MEDIAN SECTION 7.4 BOXPLOTS FREE RESPONSE QUESTIONS 31. Describe which numerical summaries (statistics) of a dataset a boxplot is based upon. ANSWER: THE FIVE-NUMBER SUMMARY (LOWEST NUMBER, LOWER QUARTILE, MEDIAN, UPPER QUARTILE, AND HIGHEST NUMBER). 32. Name two uses of a boxplot. ANSWER: 1) IT IS A VISUALLY APPEALING AND USEFUL WAY TO PRESENT A FIVE-NUMBER SUMMARY OF A DATASET; 2) IT ALLOWS FOR EASY COMPARISON OF THE CENTER AND SPREAD OF DATA COLLECTED FROM TWO OR MORE GROUPS. For Questions 33-34, use the following narrative Narrative: Liberal arts costs A random sample of 25 liberal arts colleges in the U.S. was selected, and the average cost per student was recorded for each school. The following five-number summary was calculated for this data set: lowest = $17,554; lower quartile = $23,115; median = $26,668; upper quartile = $45,879; highest = $102,262. 33. {Liberal arts costs narrative} Make a boxplot of this data set and use it to discuss the shape of the data. ANSWER: BOXPLOT SHOULD HAVE A BOX AROUND THE UPPER AND LOWER QUARTILES WITH A LINE DOWN THE MIDDLE FOR THE MEDIAN, AND LINES GOING OUT TO THE LOWEST AND HIGHEST VALUES, CONNECTING WITH THE BOX, ALL IN THE PROPER SCALE. SHAPE: SKEWED RIGHT. 34. {Liberal arts costs narrative} Using the definition of outlier discussed in your textbook, is there an outlier in this data set? Explain your answer. ANSWER: YES. THE HIGHEST AMOUNT, $102,262 IS MORE THAN 1.5 TIMES THE IQR AWAY FROM THE UPPER END OF THE BOX. MULTIPLE CHOICE QUESTIONS 35. How do you calculate the interquartile range for a data set? a. Take the highest value minus the lowest value and divide it by four. b. Subtract the value of the lower quartile from the upper quartile. c. Subtract the value of the upper quartile from the lower quartile. d. Divide the data set into four equal parts and find the range between each of the resulting quarters. ANSWER: B 36. If the width of a box in a boxplot is very large, compared to the rest of the boxplot, what does that mean about the shape of the data set? a. The data are very spread out in the middle. b. The data are clumped tightly in the middle. c. The data are not symmetric. d. Not enough information to tell. ANSWER: A 37. Suppose you look at two boxplots comparing the weights of male cats vs. female cats, and you find that the box for the males is much wider than the box for the females. What does this mean about the data sets? a. Male cats weigh more than female cats overall. b. Male cats have more variability in their weights than female cats. c. Weights of male cats are more skewed than for female cats. d. None of the above. ANSWER: B 38. Which a. Mean of the following can not be obtained from a boxplot? b. Median c. IQR d. Range e. All of the above can be obtained from a boxplot. ANSWER: A FILL-IN-THE-BLANK QUESTIONS 39. The __________ is the distance between the lower and upper quartiles in a boxplot. ANSWER: INTERQUARTILE RANGE 40. A(n) __________ is any value that is more than 1.5 times the IQR from the closest end of the box in a boxplot. ANSWER: OUTLIER SECTION 7.5 TRADITIONAL MEASURES: MEAN, VARIANCE, AND STANDARD DEVIATION FREE RESPONSE QUESTIONS For Questions 41-42, use the following narrative Narrative: Create data Suppose you can create your own data set by choosing from the numbers 1, 2, 3, 4, and 5. You can repeat a number as many times as you wish, as long as your final data set contains four numbers in it. Here are two examples of data sets you could create: {1, 2, 3, 4} or {1, 1, 5, 5}. 41. {Create data narrative} Create a data set that has the lowest possible standard deviation. ANSWER: ANY DATA SET CONTAINING THE SAME 4 NUMBERS IS ACCEPTABLE. EXAMPLE: 1, 1, 1, 1. 42. {Create data narrative} Create a data set that has mean 3 and standard deviation 0. ANSWER: 3, 3, 3, 3. 43. Which of the following two data sets has the larger standard deviation: Data Set A= {1, 1, 5, 5} or Data Set B= {1, 3, 3, 5}? ANSWER: DATA SET A 44. Explain what is meant by the standard deviation in terms that a non-statistician would understand. ANSWER: THE AVERAGE DISTANCE OF THE OBSERVED VALUES FROM THEIR MEAN (ROUGHLY). MULTIPLE CHOICE QUESTIONS 45. What is the relationship between the variance and the standard deviation? a. The variance is the square root of the standard deviation. b. The variance is the square of the standard deviation. c. The variance is twice the standard deviation. d. There is no relationship between them. ANSWER: B 46. Suppose a data set is skewed left. What is the most likely relationship between the mean and the median? a. The mean is larger than the median. b. The mean is smaller than the median. c. The mean and the median are not related to each other at all. d. The mean and the median are essentially equal. ANSWER: B 47. Which of the following statements is false? a. If the standard deviation is positive, the mean must be positive. b. The standard deviation can be negative. c. If the mean is large, the standard deviation will be large also. d. All of the above are false. ANSWER: D 48. Which of the following is not a measure of spread or variability in a data set? a. Standard deviation b. IQR c. Range d. All of the above are measures of spread or variability in a data set. ANSWER: D FILL-IN-THE-BLANK QUESTIONS 49. Because the __________ can be distorted by high outliers, the center of a data set involving incomes or prices is usually summarized using the __________. ANSWERS (RESPECTIVELY): MEAN, MEDIAN 50. If the shape of a data set is __________ then the mean and the median should be about equal. ANSWER: SYMMETRIC SECTION 7.6 CAUTION: BEING AVERAGE ISN’T NORMAL FREE RESPONSE QUESTIONS 51. What is wrong with the following statement: “Today’s temperature of 101 in Los Angeles was a record high for October, a whopping 17 degrees above normal for this date.” ANSWER: THE WORD ‘NORMAL’ IS BEING CONFUSED WITH THE WORD ‘A VERAGE.’ 52. If you just use an average to describe a set of measurements, is this enough? Explain your answer. ANSWER: NO; YOU ALSO NEED TO ADDRESS THE AMOUNT OF VARIABILITY IN THE DATA. MULTIPLE CHOICE QUESTIONS 53. Which of the following statements is statistically correct? a. “Jimmy is taller than normal for a two-year old.” b. “Jimmy is taller than the average two-year old.” c. “Jimmy is taller than the average height of two-year olds.” d. All of the above are statistically correct. ANSWER: C 54. Which of the following methods is the most appropriate one for ‘proving’ someone cheated on a multiple choice exam who was allegedly looking at someone else’s paper? a. Examine the two papers and see how many questions they both got wrong, and how many times the same wrong answer was chosen for those questions. b. Take the student’s paper that was allegedly copied from (student X) and compare it to all other students’ papers in the class. Take the number of answers that each student matched with student X and make a histogram. Then see where the alleged cheater fell on the resulting histogram. c. Neither of these methods is appropriate. There is always a chance that two people could have the same answers but no cheating was going on. d. Both of these methods are equivalent, so either one is appropriate. 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