Seeing through statistics 4th edition utts test bank by april.lavender117

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CHAPTER 9 PLOTS, GRAPHS, AND PICTURES SECTION 9.1 WELL-DESIGNED STATISTICAL PICTURES FREE RESPONSE QUESTIONS 1.

What is the purpose of a plot, graph, or picture of data? ANSWER: TO GIVE YOU A QUICK VISUAL SUMMARY OF THE DATA THAT IS MORE INFORMATIVE THAN LOOKING AT A COLLECTION OF NUMBERS.

Name three basic characteristics that a good plot, graph, or picture of data should exhibit. ANSWER: ANY 3 OF THE FOLLOWING: 1) DATA SHOULD STAND OUT CLEARLY; 2) LABELING SHOULD BE COMPREHENSIVE AND CLEAR; 3) A SOURCE SHOULD BE GIVEN FOR THE DATA; AND 4) AS LITTLE “CHART JUNK” AS POSSIBLE.

For Question 3, use the following narrative Narrative: Lottery dollar Suppose you came across the following graph in the paper, accompanied by an article on where each dollar spent on lottery tickets goes.

{Lottery dollar narrative} This graph has a problem, according to the four characteristics that any good graph should have. What is the problem with this graph? ANSWER: THERE IS NO SOURCE GIVEN FOR THE DATA.

MULTIPLE CHOICE QUESTIONS 4.

Which of the following is not a characteristic of a good plot, graph, or picture of data? a. A source must be given for the data.

The picture should contain as much information, color, and extra material as possible to keep readers interested. c. The labels should be clear and informative. d. All of the above are good characteristics of a good plot, graph, or picture of data. ANSWER: B 5.

Which of the following is not true about the plots, graphs, or pictures of data that you come across in the media? a. Most of these pictures can give you a clear, quick visual summary of that data. b. One purpose is to convey a message more quickly than if you had to study the data on your own. c. Very few of the pictures are misleading because they are checked for accuracy and fairness before being presented. d. None of the above. ANSWER: C

Which of the following should be indicated by the labels on a graph? a. The title or purpose of the picture. b. What each of the axes, bars, pie segments, etc., denotes. c. The scale of each axis, including starting points. d. All of the above. ANSWER: D

SECTION 9.2 PICTURES OF CATEGORICAL DATA FREE RESPONSE QUESTIONS 7.

What is one advantage of a bar graph over a pie chart? ANSWER: A BAR GRAPH IS MUCH MORE VERSATILE. IT CAN BE USED TO REPRESENT ACTUAL FREQUENCIES INSTEAD OF PERCENTAGES, AND TO REPRESENT PROPORTIONS THAT ARE NOT REQUIRED TO SUM TO 100%.

It is easy to be misled by pictograms. Explain how. ANSWER: TO AVOID DISTORTING THE PICTURES, THE HEIGHTS ARE OFTEN PUT IN PROPER PROPORTION, BUT THEN THE AREAS BECOME INFLATED, MISLEADING THE READER.

What type of data situation is best for using a pie chart (discuss type of data and number of variables)? ANSWER: ONLY ONE CATEGORICAL VARIABLE.

10. The focus of each type of data picture for categorical data is conveying information about the relative size of groups compared to each other. Explain what is meant by ‘relative size.’ ANSWER: THE PERCENTAGE OF THE WHOLE THAT FALLS INTO EACH GROUP (COMPARED TO JUST THE NUMBER IN EACH GROUP).

MULTIPLE CHOICE QUESTIONS

11. Which of the following is not a type of picture for organizing categorical data? a. A pie chart. b. A bar graph. c. A pictogram. d. A histogram. ANSWER: D 12. The following is an example of what type of data picture?

a. A pie chart. b. A bar graph. c. A pictogram. d. A line graph. ANSWER: A 13. The following is an example of what type of data picture?

a. A pie chart. b. A bar graph. c. A pictogram. d. A line graph. ANSWER: B

14. Which of the following is not possible to include on a bar graph? a. Frequency in each category for a categorical variable. b. Information representing two or three categorical variables simultaneously. c. Proportions that are not required to sum to 100%. d. All of the above are possible with a bar graph. ANSWER: D

FILL-IN-THE-BLANK QUESTIONS 15. A __________ can be used to represent two or three categorical variables simultaneously. ANSWER: BAR GRAPH 16. A __________ is like a bar graph except that it uses pictures related to the topic of the graph. ANSWER: PICTOGRAM

SECTION 9.3 PICTURES OF MEASUREMENT VARIABLES FREE RESPONSE QUESTIONS 17. Name three types of statistical pictures that are used to represent measurement data. ANSWER: ANY 5 OF THE FOLLOWING ARE OK: 1) HISTOGRAM; 2) STEMPLOT; 3) LINE GRAPH; 4) SCATTERPLOT; OR 5) BOXPLOT. 18. What does each dot on a scatterplot represent, in terms of both the individuals and their measurements? ANSWER: EACH DOT REPRESENTS ONE INDIVIDUAL, AND ITS CORRESPONDING PAIR OF MEASUREMENTS (SUCH AS HEIGHT AND WEIGHT). 19. Although a scatterplot can be more difficult to read than a line graph, it displays more information. Explain why. ANSWER: A SCATTERPLOT SHOWS OUTLIERS, AS WELL AS THE DEGREE OF VARIABILITY THAT EXISTS FOR ONE VARIABLE AT EACH LOCATION OF THE OTHER VARIABLE. 20. Name a situation in which a scatterplot is most useful for displaying measurement data. ANSWER: 1) FOR DISPLAYING THE RELATIONSHIP BETWEEN TWO MEASUREMENT VARIABLES.

MULTIPLE CHOICE QUESTIONS 21. The following is an example of what type of data picture?

a. A pie chart. b. A scatterplot. c. A pictogram. d. A line graph. ANSWER: D

Temeprature (degrees Fahrenheit)

22. The following is an example of what type of data picture?

90 80 70 60 50 40 30 20 10 0 0

# Cricket Chirps per 15 seconds

a. A line graph. b. A scatterplot. c. A Cartesian coordinate graph. d. None of the above. ANSWER: B 23. Measurement data displayed in terms of how they change over time can not be represented by what type of statistical picture? a. A line graph. b. A bar graph. c. A histogram. d. All of the above can be used.

ANSWER: C 24. What characteristics do statistical pictures of measurement data allow us to examine? a. Trends or patterns in the data. b. Variability in the data. c. The overall shape of the data. d. All of the above. ANSWER: D

FILL-IN-THE-BLANK QUESTIONS 25. A(n) __________ is useful for displaying the relationship between two measurement variables. ANSWER: SCATTERPLOT 26. A(n) __________ is a good way to represent measurement data as it changes over time. ANSWER: LINE GRAPH

SECTION 9.4 PICTURES OF TRENDS ACROSS TIME FREE RESPONSE QUESTIONS 27. Name one way in which a time series plot can be misleading. ANSWER: ANY REASONABLE ANSWER OK; EXAMPLES: 1) TIME LINE TOO SHORT TO GET A FULL PICTURE OF THE FLUCTUATION THAT COULD OCCUR; 2) STARTING THE DATA AT AN ADVANTAGEOUS POINT (FOR EXAMPLE, WHEN THE STOCK PRICE STARTED GOING UP). 28. What two things should you check regarding the timeline of a time series in order to avoid being misled? ANSWER: 1) THE LENGTH OF THE TIMELINE; 2) THE STARTING POINT 29. Most time series contain the same four components Name two of them. ANSWER: ANY TWO OF THE FOLLOWING: 1) LONG-TERM TREND; 2) SEASONAL COMPONENTS; 3) IRREGULAR CYCLES; OR 4) RANDOM FLUCTUATIONS. 30. Why is it important for a manufacturer to know about any seasonal component to the time series of the sales of their product? ANSWER: IF THEY DON’T KNOW THIS INFORMATION, THEY MIGHT MISTAKE INCREASED SALES AS A LONG TERM TREND AND OVERPRODUCE THEIR PRODUCT, FOR EXAMPLE. 31. How can a time series plot mislead the reader into thinking that a trend in the data is long term, when in fact it is only short term? ANSWER: BY ONLY SHOWING A SMALL TIME PERIOD ON THE TIME SERIES PLOT; THE PART THEY WANT YOU TO SEE. 32. Even if you were to account for the trend, seasonal components, and smooth irregular cycles, you would still not be able to perfectly explain or predict a time series plot. Why not?

ANSWER: RANDOM FLUCTUATIONS ARE PART OF THE NATURAL VARIABILITY PRESENT IN ALL MEASUREMENTS. 33. Name two questions you should ask to avoid being misled when reading time series data. ANSWER: ANY TWO OF THE FOLLOWING ARE OK: 1) ARE THE TIME PERIODS EQUALLY SPACED? 2) IS THE SERIES ADJUSTED FOR INFLATION? 3) ARE THE VALUES SEASONALLY ADJUSTED? 4) IS THE TIME LINE LONG ENOUGH? 5) IS THERE AN UPWARD OR DOWNWARD TREND? 6) ARE THERE OTHER SEASONAL COMPONENTS THAT HAVE NOT BEEN REMOVED? 7) ARE THERE SMOOTH CYCLES? 34. Explain why it is not wise to forecast a trend very far into the future. ANSWER: WHAT APPEARS AS A TREND IN A SHORTER TIME SERIES MAY ACTUALLY BE PART OF A CYCLE IN A LONGER TIME SERIES.

MULTIPLE CHOICE QUESTIONS 35. Which of the following does not describe a time series? a. A time series is a record of a variable across time. b. A time series is usually measured at equally spaced time intervals. c. A time series is a data set on numerous individuals measured in units of time (for example, time until completion of the obstacle course; or time until graduation). d. All of the above describe a time series. ANSWER: C 36. How does a time series plot differ from a histogram? a. A histogram displays one measurement variable, but a time series plot displays data with two measurement variables (time is one of them). b. A histogram displays data collected at one point in time, while a time series plot displays data collected over a series of times. c. If a histogram is flat, that indicates more variability than if it were bell-shaped. If a time series plot is flat, that indicates less variability than if it were bell-shaped. d. All of the above. ANSWER: D 37. Which of the following does not describe a time series plot with an irregular cycle? a. It repeatedly goes up and back down smoothly, but with an irregular pattern so as not to be predictable. b. It randomly fluctuates with no pattern at all. c. Its irregularity can often be explained by outside factors such as political or social situations. d. All of the above. ANSWER: B 38. Which of the following components of a time series plot is defined as what’s left over when the other three components have been removed? a. Random fluctuations b. Seasonal components c. Irregular cycles d. Long-term trend ANSWER: A 39. Which of the following describes the result of seasonally adjusting a time series (such as the unemployment rate)? a. The seasonal extremes have been removed.

b. One time period no longer dominates each year as the high or the low. c. The variability is reduced. d. All of the above. ANSWER: D 40. Suppose the President is campaigning for reelection, and says you should vote for him because a downward trend in the unemployment rate has occurred over the last four years. What can you conclude? e. This trend will likely continue for a long time whether the president is reelected or not. f. This trend could just be a part of the longer-term, up and down behavior of unemployment rates. g. This trend was definitely caused by the President and his administration. He should be reelected if you expect it to continue. h. None of the above. ANSWER: B

FILL-IN-THE-BLANK QUESTIONS 41. If a long-term trend in a time series plot is linear, we can estimate it by finding a regression line, with time period as the __________ variable. ANSWER: EXPLANATORY 42. Many time series measure variables that either increase or decrease steadily across time. This steady change is called a(n) __________. ANSWER: TREND

SECTION 9.5 DIFFICULTIES AND DISASTERS IN PLOTS, GRAPHS, AND PICTURES FREE RESPONSE QUESTIONS 43. Name two of the five most common problems in plots, graphs and pictures. ANSWER: ANY TWO OF THE FOLLOWING: 1) ONE OR MORE AXES NOT LABELED; 2) NOT STARTING AT ZERO; 3) CHANGES IN LABELING ON ONE OR MORE AXES; 4) MISLEADING UNITS OF MEASUREMENT; OR 5) USING POOR INFORMATION. 44. What is wrong with the following histogram?

State Populations (2000 Census)

F R E Q U E N C Y

35 30 25 20 15 10 5 0 Population Size

ANSWER: THE HORIZONTAL AXIS HAS NO UNITS LABELED. For Questions 45-46 use the following narrative: Narrative: Average hourly earnings The graph below, done in 1998 by the Bureau of Labor Statistics, represents the average hourly earnings of U.S. workers from 1947-1998 (in 1998 dollars).

45. {Average hourly earnings narrative} The designers of this graph expressed all their data in terms of 1998 dollars. Explain why they did this, and whether or not you think this is a good idea. ANSWER: IT IS IMPORTANT TO USE FAIR AND COMPARABLE UNITS OF MEASUREMENT, AND CONVERTING ALL WAGES TO 1998 DOLLARS DOES THAT. 46. {Average hourly earnings narrative} Describe the scale used on the vertical axis and whether or not it is appropriate. ANSWER: THE SCALE STARTS AT $6 AND GOES BY INCREMENTS OF $3 WITH LOTS OF SPACE BETWEEN EACH ONE. THIS MAY EXAGGERATE THE DIFFERENCES FROM YEAR TO YEAR.

MULTIPLE CHOICE QUESTIONS 47. In what way(s) can a poorly done pie chart be misleading? a. Changes in labeling on one or more axes. b. Not starting at zero as a way to exaggerate trends. c. Using poor information. d. All of the above. ANSWER: C 48. In what way(s) can a poorly done histogram be misleading? a. Changes in labeling on one or more axes. b. Not starting at zero as a way to exaggerate trends. c. Using poor information. d. All of the above. ANSWER: D 49. Suppose you have data on the number of accidents at a certain intersection for the following years: 1960, 1965, 1975, and 1990. What is the best way to display this information fairly? a. A bar graph with one bar for each year of data available; the bars are an equal distance apart. b. A line graph with the years from 1960 through 1990 marked off in equal increments and dots on the line graph representing the number of accidents for the years for which data are available. The dots are connected with lines. c. A pie chart with a slice for the percentage of accidents occurring in each of the four years for which data is available. d. Any of the above. ANSWER: B 50. If the scale on the vertical axis is in very large increments with very little space between each one, what does this do to the appearance of the data? a. It makes differences appear smaller than they really are. b. It makes differences appear larger than they really are. c. It does nothing to affect the appearance of the data. d. It makes the information easier to read and understand. ANSWER: A

FILL-IN-THE-BLANK QUESTIONS 51. A statistical picture isn’t worth much if the __________ can’t be trusted. ANSWER: DATA (OR SOURCE, INFORMATION) 52. Units of measurement are important. If a graph showed the number of crimes in each state for a given year, this would be misleading; the __________ should be reported instead. ANSWER: CRIME RATE; NUMBER OF CRIMES PER CAPITA; NUMBER OF CRIMES PER 100,000 PEOPLE, ETC.

SECTION 9.6 A CHECKLIST FOR STATISTICAL PICTURES FREE RESPONSE QUESTIONS

53. Name 3 of the 12 questions you should ask when you look at a statistical picture, before trying to interpret it. ANSWER: ANY 3 OF THE FOLLOWING ARE OK: 1) DOES THE MESSAGE STAND OUT? 2) IS THE PURPOSE EVIDENT? 3) IS THE SOURCE GIVEN? 4) IS THE SOURCE BELIEVABLE? 5) IS IT CLEARLY LABELED? 6) DO THE AXES START AT ZERO? 7) FOR TIME SERIES DATA, IS A LONG ENOUGH TIME PERIOD SHOWN? 8) CAN OBSERVED TRENDS BE EXPLAINED BY ANOTHER VARIABLE? 9) DO THE AXES KEEP A CONSISTENT SCALE? 10) ARE THERE ANY BREAKS IN THE NUMBERS? 11) IS FINANCIAL DATA ADJUSTED FOR INFLATION? 12) IS THERE “CHART JUNK”? For Questions 54-55 use the following narrative Narrative: Pick 3 lottery The Kansas Pick 3 Lottery results through 3/15/97 are shown in the table below. In this game, three numbers are drawn each week, and numbers can be repeated (such as 2, 3, 3).

Number drawn 0 1 2 3 4 5 6 7 8 9

Number of times drawn 485 468 513 491 484 480 487 482 475 474

Percentage of times drawn 10.0% 9.7% 10.6% 10.1% 10.0% 9.9% 10.0% 10.0% 9.8% 9.8%

54. {Pick 3 lottery narrative} Using the number of times each number was drawn, display the data in a bar graph that looks as though the number 1 was chosen much less often, and number 2 much more often, than the other numbers. (This will be a misleading graph.) Explain why the lottery chose to display their data in a similar way in their newsletter. ANSWER: THE GRAPH SHOULD HAVE AN EXAGGERATED SCALE, SHOWING THE HEIGHT OF THE BAR FOR NUMBER 1 BEING VERY LOW, AND THE HEIGHT OF THE BAR FOR 2 BEING VERY HIGH, COMPARED TO THE OTHER BARS. REASON: TO GIVE THE APPEARANCE THAT THERE IS SOMETHING ‘INTERESTING’ GOING ON; THAT YOU SHOULD PLAY, AND PICK 2 BECAUSE IT’S ‘HOT’ OR PICK 1 BECAUSE IT’S ‘DUE TO COME UP.’ NEITHER OF THESE IS TRUE. 55. {Pick 3 lottery narrative} Display the data in a bar graph that makes the point that each number is drawn about the same percentage of the time. ANSWER: THE GRAPH SHOULD HAVE AN APPROPRIATE SCALE, SHOWING THE BARS FOR ALL NUMBERS TO BE ABOUT EQUAL IN HEIGHT. HEIGHTS REPRESENT THE PERCENTAGE OF TIMES EACH NUMBER WAS DRAWN.

MULTIPLE CHOICE QUESTIONS

56. Which of the following is not a characteristic of a good plot, graph, or picture of data? a. Financial data collected over time should be adjusted for inflation. b. Any breaks between years where data is missing should be closed in and not left as empty spaces. c. The labels should be clear and informative. d. All of the above are good characteristics of a good plot, graph, or picture of data. ANSWER: B 57. Which of the following is not true about a plot, graph, or picture of data? a. Extraneous information should be excluded; the more extra information on a graph, the more confusing it can get. b. Many graphs are misleading; the public must look at them critically before trying to interpret their results. c. The scale on a graph doesn’t matter. Measurement data can be displayed using any scale as long as that scale is consistent. d. All of the above statements are true. ANSWER: C 58. Which of the following would automatically mean a statistical picture is misleading? a. A histogram where the scale is very large. b. A pictogram where all money is converted to current U.S. dollar amounts. c. A line graph where the axes do not start at zero. d. None of the above. ANSWER: D

REFERENCES FOR GRAPHS USED IN THIS CHAPTER Questions 3, 12: Ohio Lottery http://www.ohiolottery.com/ Question 13, 21, 29, 30: Bureau of Labor Statistics http://www.wa.gov/esd/lmea/occdata/oeswage/Page2067.htm Question 22: "Cricket Thermometers," Field & Stream, July 1993, Vol. 98 Issue 3, p21. Data excerpt from: The Songs of the Insects, (1949), by George W. Pierce, Harvard University Press, pp.12-21. Question 45: U.S. Census Bureau http://eire.census.gov/popest/data/states/tables/ST-EST2002-01.php