Collecting and Displaying Data - OGLESBY MATHrgoglesby.weebly.com/uploads/3/7/3/6/37367927/24...a...
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186 Unit 3: Descriptive Statistics LESSON Duplicating this page is prohibited by law. © 2014 Triumph Learning, LLC UNDERSTAND Oſten, one of the first steps to answering a question is collecting data For example, suppose you wanted to know how tall bean plants grow in sunny conditions To answer this question, you could find some bean plants on a farm or growing in the wild or anywhere that gets plenty of sunlight and record their heights This is an example of an observational study However, another option is to grow bean plants of your own You could grow some bean plants on your windowsill and some others in a dark closet Aſter a time, record their heights This is an example of an experimental study In this study, you directly controlled the conditions that affect the plants, such as temperature, water, and soil, so that the results depended only on the amount of light that the plants received UNDERSTAND No matter what type of study you choose, it helps to organize your data in a data display If the data are numerical and you have relatively few data points, a dot plot may be a good way to display them The base of a dot plot is a number line that lists the possible values of the data Each data point is represented by a dot placed over its value on the number line A sample dot plot is shown below Heights of Plants (in cm) 17.0 17.5 18.0 18.5 19.0 19.5 20.0 ••• • • • ••• • • • • • • • • • • • • • A histogram, another kind of data display, groups data points into ranges and shows how many of the data points fall in each range All ranges or intervals in a histogram are of equal size, and they do not overlap The sample histogram below shows the same data as in the dot plot above Height (in cm) Heights of Plants Frequency 10 7 8 9 4 5 6 3 2 1 0 17–17.9 18–18.9 19–19.9 20–20.9 24 Displaying and Analyzing Data Collecting and Displaying Data
Transcript of Collecting and Displaying Data - OGLESBY MATHrgoglesby.weebly.com/uploads/3/7/3/6/37367927/24...a...
186 Unit 3: Descriptive Statistics
LESSON
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UNDERSTAND Often,oneofthefirststepstoansweringaquestioniscollectingdata .Forexample,supposeyouwantedtoknowhowtallbeanplantsgrowinsunnyconditions .Toanswerthisquestion,youcouldfindsomebeanplantsonafarmorgrowinginthewildoranywherethatgetsplentyofsunlightandrecordtheirheights .Thisisanexampleofanobservational study .
However,anotheroptionistogrowbeanplantsofyourown .Youcouldgrowsomebeanplantsonyourwindowsillandsomeothersinadarkcloset .Afteratime,recordtheirheights .Thisisanexampleofanexperimental study .Inthisstudy,youdirectlycontrolledtheconditionsthataffecttheplants,suchastemperature,water,andsoil,sothattheresultsdependedonlyontheamountoflightthattheplantsreceived .
UNDERSTAND Nomatterwhattypeofstudyyouchoose,ithelpstoorganizeyourdatainadatadisplay .Ifthedataarenumericalandyouhaverelativelyfewdatapoints,adot plotmaybeagoodwaytodisplaythem .Thebaseofadotplotisanumberlinethatliststhepossiblevaluesofthedata .Eachdatapointisrepresentedbyadotplacedoveritsvalueonthenumberline .Asampledotplotisshownbelow .
Heights of Plants (in cm)
17.0 17.5 18.0 18.5 19.0 19.5 20.0
• • ••
••
• • ••••
• •• • •••••
•
Ahistogram,anotherkindofdatadisplay,groupsdatapointsintorangesandshowshowmanyofthedatapointsfallineachrange .Allrangesorintervalsinahistogramareofequalsize,andtheydonotoverlap .Thesamplehistogrambelowshowsthesamedataasinthedotplotabove .
Height (in cm)
Heights of Plants
Freq
uenc
y
10
789
456
3210
17–17.9 18–18.9 19–19.9 20–20.9
24 Displaying and Analyzing Data
Collecting and Displaying Data
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Lesson 24: Displaying and Analyzing Data 187
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Thechairmanofacompanyaskedhischieffinancialofficertotracktheclosingpriceofthecompany’sstockover20tradingdays .Thestockprices,indollars,arelistedbelow .
26 .70,26 .50,26 .90,26 .70,26 .60,25 .50,25 .10,25 .30,25 .10,26 .50,
27 .40,26 .60,26 .80,26 .70,26 .70,27 .60,27 .40,27 .80,27 .60,27 .90
Createahistogramforthestockpricedata .
Chooseatitleandintervalsforthehistogram .
Titlethehistogram“StockPrices .”
Giventhespreadofprices,intervalsof50centswillworkwellforthedata .
1
Createthehistogram .
Usethefrequenciestomakeabarforeachinterval .
▸
Price (in dollars)
Stock Prices
Freq
uenc
y
10
8
6
4
2
0
25.0
0–25
.49
25.5
0–25
.99
26.5
0–26
.99
27.0
0–27
.49
27.5
0–27
.99
26.0
0–26
.49
3
Groupthedataintointervalsandcountthefrequencies .
Price Intervals
Data Points Frequency
25 .00–25 .4925 .10,25 .30,25 .10
3
25 .50–25 .99 25 .50 1
26 .00–26 .49 0
26 .50–26 .99
26 .70,26 .50,26 .90,26 .70,26 .60,26 .50,26 .60,26 .80,26 .70,26 .70
10
27 .00–27 .49 27 .40,27 .40 2
27 .50–27 .9927 .60,27 .80,27 .60,27 .90
4
2
Whataresomeadvantagesofusingadotplotinsteadofahistogram?
DISCUSS
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188 Unit 3: Descriptive Statistics
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UNDERSTAND Youcanusethedistributionofadataset,oritsshape,tointerpretitandtocompareittootherdatasets .Fourkindsofdistributionsaredescribedbelow .
•Normal distribution:Thedatasethasoneclearpeakinthecenterwithotherdatapointsspreadequallyonbothsidesofthepeak .Becauseofitsappearance,thiskindofdistributionissometimesreferredtoasabellcurve .Anormaldistributioncanalsobecalledasymmetricdistribution .
•Skewed distribution:Thedatasethasoneclearpeak .Butinsteadofbeingspreadequallyoneithersideofthepeak,mostorallofthedataareconcentratedononesideofthepeak .Thiskindofdistributionissaidtohavea“tail .”Dependingonthedirectionofthetail,thedatacanbedescribedasskewedrightorskewedleft .Theskeweddistributionshownbelowisskewedtotheleft .
•Bimodal distribution:Thedatasethastwoclearpeaks .
•Uniform distribution:Thedataitemsareequallyspreadacrosstherangeofthedataset,andtherearenoclearpeaks .
Examplesofeachofthesekindsofdistributionaregraphedbelow .
Normal Distribution Skewed Distribution
Bimodal Distribution Uniform Distribution
Data Distributions
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Lesson 24: Displaying and Analyzing Data 189
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Theweights,inpounds,ofagroupofcatsenteredinacatshowaregivenbelow .
11__2,2,2,3,3,4,4,4,41__2,5,5,5,51__2,53__4,
6,6,6,6,61__4,61__2,7,7,7,7,71__2,73__4,8,
8,81__2,81__2,9,9,91__4,93__4,10,10,101__2,11,13
Usethedatatoconstructahistogram .Thendescribethedistributionofthedata .
Chooseintervalsforyourhistogram .
Theweightsrangefrom11__2to13pounds .Intervalsof2poundswouldbeagoodchoice .
1
Dividethedataintointervalsandcountfrequencies .
Weight (w) Intervals
Data Points (in lb)
Frequency
0#w,2 11__2 1
2#w,4 2,2,3,3 4
4#w,64,4,4,41__2,5,5,
5,51__2,53__49
6#w,86,6,6,6,61__4,61__2,
7,7,7,7,71__2,73__412
8#w,108,8,81__2,81__2,9,9,
91__4,93__48
10#w,12 10,10,101__2,11 4
12#w,14 13 1
Noticethateachintervalincludesitslowerboundaryvalue,butnottheupperboundary .So,onthehistogram,thebarlocatedbetween2and4willincludedatapointsof2lb,butnot4lb .
2
Constructthehistogram .Thendescribethedistribution .
▸
Weight (in pounds)
Weights of Cats
Freq
uenc
y
12
10
8
6
4
2
00 2 4 6 8 10 161412
Thehistogramhasoneclearpeak,andtherestofthedataarespreadrelativelyequallyonbothsidesofthepeak .Thedatashowanormaldistribution .
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Howwouldthedatahavetochangetoshowaskeweddistribution?Abimodaldistribution?
DISCUSS
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EXAMPLE A ThelistbelowshowshowmanypointsCorinnascoredineachof16basketballgames:
8,3,3,9,4,7,10,4,5,9,5,7,6,8,10,6
MakeadotplotofCorinna’spoints .
Choosearangeandtitleforthedotplot .
Titletheplot“Corinna’sPointsScored .”
Theleastvalueis3,andthegreatestvalueis10 .
Anumberlinefrom0to14willincludeallthedata .
Choosearangeandtitleforthedotplot .
Titletheplot“Leanne’sPointsScored .”
Theleastvalueis5,andthegreatestvalueis14 .
UsethesamerangethatyouusedforCorinna’sdotplot .
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1
Ploteachdatapointaboveanumberline .
Foreachelementinthedataset,placeadotaboveitsvalueonthenumberline .Ifmultiplepointshavethesamevalue,stackthedotsontopofoneanother .
▸ Corinna’s Points Scored
0 2 4 6 8 10 12 14
• • • • • • • •• • • • • • ••
Ploteachdatapointabovethenumberline .
▸ Leanne’s Points Scored
0 2 4 6 8 10 12 14
• • • • • •• • •
•• • • •
• •
2
2
LeanneisonCorinna’steam .ThelistbelowshowshowmanypointsLeannescoredinthesame16basketballgames:
13,14,9,12,13,13,14,10,9,12,6,5,7,11,10,8
MakeadotplotofLeanne’spoints .
Comparetheshapesofthedotplots .WhatdotheirshapestellyouaboutthedistributionsofCorinna’sandLeanne’sscores?
DISCUSS
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Lesson 24: Displaying and Analyzing Data 191
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EXAMPLE B Thetwohistogramsbelowshowtheagesofwaitstaffattworestaurants .
Age (in years)
Ages of Wait Staff,Pasta Restaurant
Freq
uenc
y8
6
4
2
0
16-2
0
21-2
526
-30
31-3
536
-40
41-4
556
-60
51-5
546
-50
Age (in years)
Ages of Wait Staff,Pizza Restaurant
Freq
uenc
y
8
6
4
2
0
16–2
0
21–2
5
26–3
0
31–3
5
36–4
0
41–4
5
56–6
0
51–5
5
46–5
0
Identifythekindofdistributionshownbyeachhistogram .Usetheshapesofthedatasetstocomparethem .
Describetheshapeofthehistogramforthepastarestaurant .
Thehistogramisnearlysymmetricalandhasacentralpeakatages36–40 .
Itsshapemostcloselymatchesabellcurve .
Theagesofthewaitstaffatthepastarestaurantshowanormaldistribution .
Usetheshapesofthehistogramstointerpreteachdataset .
Thenormaldistributionofthedatafromthepastarestaurantshowsthattheagesofitswaitstaffarerelativelyevenlydistributedaroundthe36–40agerange .
Thedatafromthepizzarestaurantisskewedtotheright,andmostofthedatafallbelowthe36–40agerange .So,ingeneral,thewaitstaffofthepizzarestaurantisyoungerthanthatofthepastarestaurant .
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Describetheshapeofthehistogramforthepizzarestaurant .
Thehistogramhasonepeak .Themajorityofthedataareina“tail”thatextendstotherightofthepeak .
Theagesofthewaitstaffatthepizzarestaurantshowadistributionskewedtotheright .
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Theagesofthewaitstaffataseafoodrestaurantarelistedbelow .
18,21,23,26,26,27,28,29,30,31,35,
39,42,46,48,49,49,50,51,53,54,57
Onaseparatesheetofpaper,createahistogramforthedata .Compareitsshapetothetwohistogramsonthispage .
TRY
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Practice
192 Unit 3: Descriptive Statistics
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For questions 1 and 2, classify each study as observational or experimental.
1. Youmeasurehowmanypull-upsstudentsinyourP .E .classcanperforminoneminuteeachweekforseveralweeks .
2. Youprovidehalfofaclassofelementaryschoolstudentswith20minutesofspellingpracticeinsteadofrecess .Theotherhalfoftheclassgoestorecess .Yourecordstudents’gradesonaspellingtesttakenafterrecess .
For questions 3–5, use the given information. Create a histogram for each data set. Describe the distribution of each data set.
Studentsinthe1stand2ndperiodbiologyclassestookthesametest .Theirtestscoresarelistedbelow .
3. 1stperiodtestscores:
100,91,86,73,81,100,93,94,86,
86,99,93,98,84,80,97,93,
87,70,97,94,88,85,96,90
66–7
0
71–7
5
76–8
0
81–8
5
86–9
0
91–9
5
96–1
00x
y
0123456789
Test Score
Freq
uenc
y
1st Period Class
Distribution:
4. 2ndperiodtestscores:
81,87,95,85,83,82,76,68,86,
83,93,87,76,87,71,100,76,
91,73,80,80,84,87,88,73
66–7
0
71–7
5
76–8
0
81–8
5
86–9
0
91–9
5
96–1
00x
y
0123456789
Test Score
Freq
uenc
y
2nd Period Class
Distribution:
5. Compareandcontrastthehistogramsforthebiologyclassesinquestions4and5 .
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Lesson 24: Displaying and Analyzing Data 193
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Create a dot plot for the given data. Describe the shape of the data.
6. Nathanielopened20peanutshellsandrecordedthenumberofpeanutshefoundineachshell .
3,2,0,1,5,2,1,2,3,1,2,2,1,2,2,3,2,3,1,2
Fill in each blank with an appropriate word or phrase.
7. A_____________showsdatapointsasdotsaboveanumberline .
8. A____________showshowfrequentlydataoccurwithincertainrangesorintervals .
9. ______________usedinahistogrammustbeequal .
10. A______________distributionissymmetricandresemblesabellcurve .
11. A______________distributionhastwodistinctpeaks .
12. A______________distributionhasa“tail”thatextendsmoretoonesideofthegraphthantheother .
13. COMPARE Antoinesurveyed200highschoolstudentstofindouthowmanyhourstheysleptthispastSaturdaynightandhowmanyhourstheysleptthispastMondaynight .Thehistogramsshowthedatahecollected .
Time (in hours)
Hours of Sleep, Monday
Freq
uenc
y
70
60
50
40
30
20
10
05 6 7 8 9 10 1211
Time (in hours)
Hours of Sleep, Saturday
Freq
uenc
y
70
60
50
40
30
20
10
05 6 7 8 9 10 1211
Comparethedistributionsofdataonthetwographs .Howdotheydiffer?Forwhatreasoncouldtheybesodifferent?Explain .
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