1-5 Circle Graphs And 1-9 Misleading Graphs

Circle Graphs andMisleading Graphs1-5: Circle GraphsA circle graph, also called a pie chart, showshow a set of data is divided into parts.The entire circle contains 100% of the data.Each sector, or slice, of the circle representsone part of the entire data set.The circle graph compares the number of species ineach group of echinoderms. Echinoderms are marineanimals that live on the ocean floor. The nameechinoderm means “spiny-skinned.”1

Additional Example 1A: Life Science ApplicationAdditional Example 1B: Life Science ApplicationUse the circle graph to answer the question.Use the circle graph to answer the question.A. Which group ofechinodermsincludes the fewestnumber of species?B. Approximatelywhat percent ofechinoderm speciesare brittle stars andbasket stars?about 1 , so approximately33% 3The sector for sea lilies andfeather stars is the smallest,so this group includes thefewest number of species.Additional Example 1C: Life Science ApplicationTry This: Example 1AUse the circle graph to answer the question.Use the circle graph to answer each question.C. Which group ismade up of a greaternumber of species,sea cucumbers orsea stars?A. Which size car sold themost?The sector for sea stars islarger than the sector for seacucumbers. This means thereare more kinds of sea starsthan sea cucumbers.LuxuryLargemidsizeMidsizeSmall2

Try This: Example 1BTry This: Example 1CUse the circle graph to answer each question.B. Approximately whatpercent of cars sold weremidsize?LuxuryUse the circle graph to answer each question.LuxuryC. Which size sold less—large or small?LargeLargelargeabout 50%MidsizeMidsizeSmallSmallAdditional Example 2A: Interpreting Circle GraphsAdditional Example 2B: Interpreting Circle GraphsLeon surveyed 30 people about pet ownership. Thecircle graph shows his results. Use the graph toanswer each question.Leon surveyed 30 people about whether they ownpets. The circle graph shows his results. Use thegraph to answer each question.A. How many peopleown dogs only?B. If 60 people weresurveyed and 12people said they owndogs only, how manypeople own both catsand dogs?The circle graph showsthat 20%, or one-fifth, ofthe people own dogs only.One-fifth of 30 is 6, so sixpeople own dogs only.Since 20% is 12 people,10% is 6 people. Six peopleown both cats and dogs.3

Try This: Example 2ATry This: Example 2BFifty students were asked which instrument theycould play. The circle graph shows the responses.Use the graph to answer each question.fluteA. How many students donot play an instrument?The circle graph shows that50%, or one-half, of thestudents play no instrument.One-half of 50 is 25, sotwenty-five students do notplay an instrument.drum20%Fifty students were asked which instrument theycould play. The circle graph shows the responses.Use the graph to answer each question.flute10%piano20%B. Ten students said theyplay the piano. How manyplay the flute?noinstrument50%Since 20% is 10 students,10% is 5 students. Fivestudents play the flute.drum20%piano20%10%noinstrument50%Additional Example 3A:Choosing an Appropriate GraphAdditional Example 3B:Choosing an Appropriate GraphDecide whether a bar graph or circle graphwould best display the information. Explain youranswers.Decide whether a bar graph or circle graphwould best display the information. Explain youranswers.A. the percent of U.S. population living in thedifferent regions of the countryB. the number of tickets sold for each performanceof a community playA circle graph is the better choice because it makes iteasy to see what part of the U.S. population comesfrom the different regions of the country.A bar graph is the better choice because it makes iteasy to see how the number of tickets sold changedover each performance.4

Additional Example 3C:Choosing an Appropriate GraphDecide whether a bar graph or circle graphwould best display the information. Explain youranswers.C. the comparison between the number ofstudents on the basketball team and the totalnumber of students on all sports teamsA circle graph is the better choice because the sectorthat represents the number of students on thebasketball team could be compared to the entirecircle, which represents the total number of studentson all school sports teams.Try This: Example 3ADecide whether a bar graph or circle graphwould best display the information. Explain youranswers.A. the percent of people buying a certain color of anew vehicleA circle graph is the better choice. By looking at thesectors, it makes it easy to see what color peopleprefer.Try This: Example 3BTry This: Example 3CDecide whether a bar graph or circle graphwould best display the information. Explain youranswers.Decide whether a bar graph or circle graphwould best display the information. Explain youranswers.B. the number of visitors to the Grand Canyon forthe last ten yearsC. the comparison of different themes voted on fora school partyA bar graph is the better choice because it makes iteasy to see how the number of visitors has changedover the years.A circle graph is a better choice because it makes iteasy to see what theme people prefer.5

What does it mean to mislead someone?1-9: Misleading GraphsSome people who compile statistics and creategraphs often present the results in a way thatis favorable to their purpose.What do you think could be misleading aboutthe following statement: “Brand A is preferredtwo to one over other brand!”Graphs and statistics areoften used to persuade.Advertisers and othersmay accidentally orintentionally presentinformation in amisleading way.For example, art is often used to make agraph more interesting, but it can distortthe relationships in the data.A data display that distorts information in orderto persuade can be misleading.An axis in a graph can be “broken”to make the graph easier to read.However, a broken axis can alsobe misleading.In the graph at right, the cost perminute for service with Company Blooks like it is twice as much as thecost for service with Company A.In fact, the difference is only 0.10per minute.6

Additional Example 1A: Identifying MisleadingGraphsExplain why each graph is misleading.A.The graphsuggests that thestock will continueto increase through2020, but there’sno way to foreseethe future.Additional Example 1B: Identifying MisleadingGraphsExplain why each graph is misleading.B.Common Reasons Why a GraphMight be MisleadingAdditional Example 1C: Identifying MisleadingGraphsExplain why each graph is misleading.C.The scale is socompressed that it’shard to see anydifference among thebrands.Because the scale leavesout 0 to 100 (break in they-axis), the bar heightsmake it appear that thesixth grade sold aboutthree times as manytickets as either of theother two grades. In fact,the sixth grade sold onlyabout 20% more. There is a break in the y-axisThe scale on the y-axis does not start at zeroThe scale is compressedThe graph displays predictions (the future)There are no labels7

Try This: Example 1ATry This: Example 1BExplain why each graph is misleading.A.% of Return on InvestmentB. 150 Preferred Juice Flavors50148The graph suggeststhat the rate ofinvestment returnwill continue toincrease, but thereare no guarantees(predicting future)40302010146144142140012345*Grape6*Drink Sales10080No data from 50 to 1206040200Brand XBrand YBrand ZThis graph is toocompressed to seemuch differencebetween thebrands indicatingthat they are fairlyequal.Both line graphs show the high temperature Mondaythrough Friday. Which graph could be misleading? Why?Temperature ( F)Explain why each graph is misleading.120AppleAdditional Example 1Try This: Example 1CC.CherryThe graph appearsto indicate thatsignificantly morepeople prefer grapedrink over the otherswhen in fact there isa small margin ofdifference. (0 to140 is not graphedbreak in y-axis)* projectedHigh Temperature100755025Temperature ( F)60Explain why each graph is misleading.High Temperature908070600MTuWDayThFMTuWThFDayThe graph on the right could be misleading. Thevertical axis is broken, so differences intemperature appear greater.8

Try This: Example 1Additional Example 2A: Analyzing Misleading GraphsWhich graph could be misleading? Why?Average Restaurant Meal Price252015100Gino’s Village PastaGrillCityExplain how you could redraw the graph so itwould not be misleading.Graph BPrice per mealPrice per mealGraph ACityDiner30Draw the entire verticalscale on the graph.25201510Gino’s Village PastaGrillCityCityDinerGraph B could be misleading. The vertical axis does notbegin with zero, so differences in scales appear greater.Explain how you could redraw the graph so itwould not be misleading.Draw the vertical scale withequal spacing betweenmarks so that the distancebetween 0 and 18,000equals the distance between18,000 and 36,000.Try This: Example 2AExplain how you could redraw the graph so itwould not be misleading.Taxicab FaresDraw the entire verticalscale on the graph. Thevertical axis is broken, sodifferences in fareappear greater.13Fare ( )Additional Example 2B: Analyzing Misleading Graphs121110Mon Tue Wed Thu Fri9

Try This: Example 2BExplain how you could redraw the graph so itwould not be misleading.Can you think of any graphs youmay have seen that might havebeen misleading?Ounces of WaterWater ConsumedDraw the entire verticalscale on the graph. Thevertical axis does notstart at zero sodifferences in waterconsumed seem greater.4840322416MarkFrankMilaYvonne10

1 Circle Graphs and Misleading Graphs 1-5: Circle Graphs A circle graph, also called a pie chart, shows how a set of data is divided into parts. The entire circle contains 100% of the data. Each sector, or slice, of the ci