8-9 Misleading Statistics - Glencoe
8-9Misleading StatisticsMAIN IDEAMath Onlineglencoe.com Extra Examples Personal Tutor Self-Check QuizHOCKEY The graph shows the all-time Stanley Cup playoff leaders.1. According tothe size of thehockey players,how manytimes morepoints doesMark Messierappear to havethan Jari Kurri?Explain.All-Time Stanley Cup Playoff Leaders430380PointsRecognize whenstatistics and graphsare misleading.3302802301802. Do you PaulCoffeyPlayersthis graph isSource: ESPN Sports Almanacrepresentativeof the players’number of points? 1, 2. See margin.Graphs let readers analyze and interpret data easily, but are sometimesdrawn to influence conclusions by misrepresenting the data. The use ofdifferent scales can influence conclusions drawn from graphs.Changing the Interval of Graphs1 SCHOOL DANCES The graphs show how the price of spring danceGraph AGraph BSpring Dance TicketsSpring Dance Tickets24122010168Price ( )Price ( )tickets increased.12840’02 ’03 ’04 ’05 ’06Year6420’02 ’03 ’04 ’05 ’06YearDo the graphs show the same data? If so, explain how they differ.The graphs show the same data. However, the graphs differ in thatGraph A uses an interval of 4, and Graph B uses an interval of 2.444Chapter 8 Statistics: Analyzing Data444 0444 0449 CH08 L9 874046 4449/22/07 12:55:49 PM
Which graph makes it appear that the prices increased more rapidly?Graph B makes it appear that the prices increased more rapidly eventhough the price increase is the same.Which graph might Student Council use to show that while ticketprices have risen, the increase is not significant? Explain. Theymight use Graph A. The scale used on the vertical axis of this graphmakes the increase appear less significant.Changing ScalesTo emphasize a changeover time, reduce thescale interval on thevertical axis.a. BUSINESS The line graphs show monthly profits of a companyfrom October to March. Which graph suggests that the businessis extremely profitable? Is this a valid conclusion? Explain.Graph BMonthly ProfitsGraph AMonthly Profits15,40015,30017,00016,500Profit ( )Profit ( )a. Sample answer:Although both graphsshow a profit, in Graph A,the increase in profits isexaggerated due to theintervals of both 500and 0014,00014,0000t. v. c. n. b. r.Oc No De Ja Fe Ma0t. v. c. n. b. r.Oc No De Ja Fe MaMonthMonthSometimes the data used to create the display comes from a biasedsample. In these cases, the data and the display are both biased andshould be considered invalid.Identify Biased DisplaysDo You Use theFitness Room?company mailed a survey to 500of his employees in order todetermine if they use the fitnessroom at work. The results areshown in the graph. Identify anysampling errors and explain whythe sample and the display mightbe biased.Number of Responses2 FITNESS The president of a large500450400350300250200150100500338116sYeNoNot all of the surveys were returned since 338 116 500. This is abiased, voluntary response sample. The sample is not representativeof the entire population since only those who wanted to participate inthe survey are involved in the sampling.The display is biased because the data used to create the displaycame from a biased sample.Lesson 8-9 Misleading Statistics445 0444 0449 CH08 L9 874046 4454459/22/07 12:55:54 PM
What Do You Like to Doon a Saturday cing0vietheater asked 100 of his customerswhat they like to do on a Saturdaynight. The results are shown inthe graph. Identify any samplingerrors and explain why the sampleand the display might be biased.100Eventb. MOVIES The manager of a movieNumber of Responsesb. The sample is abiased conveniencesample. Customersat a movie theaterprobably like towatch moviesmore than otheractivities. Thedisplay is biasedbecause the dataused to create thedisplay came froma biased sample.Statistics can also be used to influence conclusions.Misleading Statistics3 MARKETING Refer to the table that gives the height of roller coastersat an amusement park. The park boasts that the average height oftheir roller coasters is 170 feet. Explain how this is misleading.Park Rollercoaster HeightsCoastermean:Height (ft)Viper109Monster135Red Zip115Tornado365Riptide126109 135 115 365 126850 55 170median: 109, 115, 126, 135, 365mode:noneThe average used by the park was the mean. This measure is muchgreater than most of the heights listed because of the outlier, 365 feet.So, it is misleading to use this measure to attract visitors.A more appropriate measure to describe the data would be themedian, 126 feet, which is closer to the height of most of the coasters.c. Sample answer:The mean price ofthe items listed is 3.50; however,they are calculatingthe average priceby including coffee,a low priced item.446c. FOOD A restaurant claims itsaverage menu price is 3.50.Use the table to explain howthis is misleading.MenuBurger 4.00Fish Sandwich 4.45Chicken Sandwich 4.35Garden Salad 3.90Coffee 0.80Chapter 8 Statistics: Analyzing Data446 0444 0449 CH08 L9 874046 4469/22/07 12:55:57 PM
Example 11. BASEBALL Refer to the graphs below. Which graph suggests that Cy Young(pp. 444–445)had three times as many wins as Jim Galvin? Is this a valid conclusion?Explain.Graph AGraph BMost Career Wins by a PitcherMost Career Wins by a chersPitchers1. Graph B; Fromthe length of thebars, it appearsthat Cy Young hadabout 3 times asmany wins as JimGalvin. However,Jim Galvin had 365wins and Cy Younghad 511 wins. So,the conclusion isnot onChristyMathewsonJimGavinJimGavin0200400600350400 450WinsWins2. PHONES The manager of a telephone550How Do You Prefer toPay Your Telephone Bill?company mailed a survey to 400households asking each household howthey prefer to pay their monthly bill.The results are shown in the graph at theright. Identify any sampling errors andexplain why the sample and the displaymight be biased. See margin.Number of ResponsesExample 2(pp. 445–446)5002001501251007550250ailreemthro tl f un Owa ccoaPdr g Aith kint W heccire CyybPaMinnlOayD(p. 446)HOMEWORKForExercises4, 85, 96, 7HELPSeeExamples1233. TUNNELS The table lists the five largest landU.S. Vehicle Tunnels on Landvehicle tunnels in the U.S. Write a convincingargument for which measure of centraltendency you would use to emphasize theaverage length of the tunnels. See margin.4. GAS The bar graphshows monthly gasprices for 2006–2007.Why is the graphmisleading?See margin.NameLength (ft)Anton Anderson Memorial13,300E. Johnson Memorial8,959Eisenhower Memorial8,941Allegheny6,072Liberty Tubes5,920Gas Prices3.53Price ( )Example Lesson 8-9 Misleading Statistics447 0444 0449 CH08 L9 874046 4474479/22/07 12:56:03 PM
5. SCHOOL To determine how often his studentsTardy to ClassNumber of Responsesare tardy, Mr. Kessler considered his first periodclass. The results are shown in the graph at theright. Identify any sampling errors and explainwhy the sample and the display might be biased.1412108642050–106–05–111–216Number of Times TardyTRAVEL For Exercises 6 and 7, use the table.Annual Sight-Seeing Visitors6. Find the mean, median, and mode of theSightdata. Which measure might be misleadingin describing the average annual numberof visitors who visit these sights? Explain.7. Which measure would be best if youwanted a value close to the most numberof visitors? Explain.Visitors*Cape Cod4,600,000Grand Canyon4,500,000Lincoln Memorial4,000,000Castle Clinton4,600,000Smoky Mountains10,200,000Source: The World Almamac*Approximation8. STOCK The graphs below show the increasesand decreases in the monthly closing prices of Skateboard Depot’s stock.'RAPH "-ONTHLY 3TOCK 0RICES5040 3020100 FeJan *AN &EB -AR !PR -AY0RICE PER 3HARE Monthly Stock Prices.b.Mar.Apr.MayPrice per Share ( )Graph AMonth-ONTHSuppose you are a stockbroker and want to show a customer that theprice of the stock has been fairly stable since January. Write a convincingargument as to which graph you should show the customer.9. MANUFACTURING To evaluate their product,EXTRAPRACTICESee pages 690, 711.44810. Rent has remained fairly stable.11. Rent has increased dramatically.10095908070605040302010320ECo xcelnd lenitio tnDoesNoaC tHha oldrgeCrac Broke kedC nas oringAPARTMENTS For Exercises 10 and 11, create adisplay that would support each argument giventhe monthly costs to rent an apartment for thelast five years are 500, 525, 560, 585, and 605.Battery ProductionPercent of Batteriesthe manager of an assembly line inspects thefirst 100 batteries that are produced out of30,000 total batteries produced that day. Hedisplays the results in the graph at the rightand then releases it to the local newspaper.Identify any sampling errors and explain whythe sample and the display might be biased.ProductChapter 8 Statistics: Analyzing Data0444 0449 CH08 L9 874046.indd 4489/24/07 5:32:23 PM
H.O.T. Problems12. CHALLENGE Does adding values that are much greater or much less thanthe other values in a set of data affect the median of the set? Give anexample to support your answer.13.WR ITING IN MATH Describe at least two ways in which the display ofdata can influence the conclusions reached.14. The bar graph shows the averagenumber of hours each week that agroup of students attend anextracurricular activity after school.15. A department store mailed 100surveys to teenagers about theirpreferred style of jeans. The graphshows the results.Number of TeenagersPreferred Style of Jeansyndes42504540353025201510504A The vertical scale should showdays instead of hours.B The graph does not show whichactivity each person attended.C The intervals on the vertical scaleare inconsistent.D The graph’s title is misleading.tsecuotBoWhich statement best tells why thegraph may be misleading if you wantto use the graph to compare thenumber of hours the students attendan extracurricular e (h)Time Spent onExtracurricular ActivitieswLoRihucSloedlaxReTypes of JeansWhich of the following is trueconcerning the sample and the display?F Both the display and the sampleare unbiased.G The display is biased because thesample is a biased, voluntaryresponse sample.H The display is biased because thesample is a biased, conveniencesample.JThe sample is biased but thedisplay is unbiased.16. CARS To determine what kind of automobile is preferred by mostcustomers, the owner of an auto dealership surveys every 10th personwho enters the dealership. Of these, 54% state that they prefer 4-doorsedans. Based on these results, if the dealership stocks 150 cars, abouthow many of them should be 4-door sedans? (Lesson 8-8)17. MP3 PLAYERS In a survey, 46% of randomly selected teens said they ownan MP3 player. Predict how many of the 850 teens at Harvey MiddleSchool own an MP3 player. (Lesson 8-7)Lesson 8-9 Misleading Statistics0444 0449 CH08 L9 874046.indd 4494499/24/07 5:32:25 PM
MAIN IDEA Recognize when statistics and graphs are misleading. Math Online glencoe.co
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fresh garden produce, honey, jams, pickles and an assort-ment of other homemade goods. The market is located on 11th Street in downtown Glencoe across from the Glen-coe City Center. Glencoe seniors to meet The Glencoe Senior Citizens group will meet Thurs-day, Oct. 10, at 12:30 p.m., at the senior room in the Glencoe City Center.
31 Misleading Graphs and Statistics It is a well known fact that statistics can be misleading. They are often used to prove a point, and can easily be twisted in favour of that point! The pur-pose of this section is to learn how to recognize common statisitcal deception so that to avoid being mislead. Bad Sampling
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