Prevention 9.2 Software McAfee Total Protection for Data Loss
MODELING DATA—9.2 9.2 Data Distribution Z · 9.2 Data Distribution ... histograms, and box plots...
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SECONDARY MATH I // MODULE 3 MODELING DATA—9.2 Mathematics Vision Project Licensed under the Creative Commons Attribution CC BY 4.0 mathematicsvisionproject.org 9.2 Data Distribution A Practice Understanding Task A lot of information can be obtained from looking at data plots and their distributions. It is important when describing data that we use context to communicate the shape, center, and spread. Shape and spread: • Modes: uniform (evenly spread- no obvious mode), unimodal (one main peak), bimodal (two main peaks), or multimodal (multiple locations where the data is relatively higher than others). • Skewed distribution: when most data is to one side leaving the other with a ‘tail’. Data is skewed to side of tail. (if tail is on left side of data, then it is skewed left). • Normal distribution and standard deviation: curve is unimodal and symmetric. Data that has a normal distribution can also describe the data by how far it is from the mean using standard deviation. • Outliers: values that stand away from the body of the distribution. For a box-and-whisker outliers determined if they are more than 1.5 times the interquartile range (length of box) beyond quartiles 1 and 3. Also considered an outliner if data is more than two standard deviations from the center of a normal distribution. • Variability: values that are close together have low variability; values that are spread apart have high variability. Center: • Analyze the data and see if one value can be used to describe the data set. Normal distributions make this easy. If not a normal distribution, determine if there is a ‘center’ value that best describes the data. Bimodal or multimodal data may not have a center that would provide useful data. There are representations of test scores from six different classes found below, for each: 1. Describe the data distribution. 2. Compare data distributions between Anderson and Williams. 3. Compare data distributions between Williams and Lemon. 4. Compare data distributions between Croft and Hurlea. 5. Compare data distributions between Jones, Spencer, and Anderson. 6. Compare data distributions between Spencer and the other histograms. 7. Which distributions are most similar? Different? Explain your answer. cc by https://flic.kr/p/5DDPFZ 5
Transcript of MODELING DATA—9.2 9.2 Data Distribution Z · 9.2 Data Distribution ... histograms, and box plots...
SECONDARY MATH I // MODULE 3 MODELING DATA—9.2
Mathematics Vision Project Licensed under the Creative Commons Attribution CC BY 4.0 mathematicsvisionproject.org
9.2 Data Distribution A Practice Understanding Task Alotofinformationcanbeobtainedfromlookingatdataplotsandtheirdistributions.Itisimportantwhendescribingdatathatweusecontexttocommunicatetheshape,center,andspread.Shapeandspread:
• Modes:uniform(evenlyspread-noobviousmode),unimodal(onemainpeak),bimodal(twomainpeaks),ormultimodal(multiplelocationswherethedataisrelativelyhigherthanothers).
• Skeweddistribution:whenmostdataistoonesideleavingtheotherwitha‘tail’.Dataisskewedtosideoftail.(iftailisonleftsideofdata,thenitisskewedleft).
• Normaldistributionandstandarddeviation:curveisunimodalandsymmetric.Datathathasanormaldistributioncanalsodescribethedatabyhowfaritisfromthemeanusingstandarddeviation.
• Outliers:valuesthatstandawayfromthebodyofthedistribution.Forabox-and-whiskeroutliersdeterminediftheyaremorethan1.5timestheinterquartilerange(lengthofbox)beyondquartiles1and3.Alsoconsideredanoutlinerifdataismorethantwostandarddeviationsfromthecenterofanormaldistribution.
• Variability:valuesthatareclosetogetherhavelowvariability;valuesthatarespreadaparthavehighvariability.
Center:• Analyzethedataandseeifonevaluecanbeusedtodescribethedataset.Normal
distributionsmakethiseasy.Ifnotanormaldistribution,determineifthereisa‘center’valuethatbestdescribesthedata.Bimodalormultimodaldatamaynothaveacenterthatwouldprovideusefuldata.
Therearerepresentationsoftestscoresfromsixdifferentclassesfoundbelow,foreach:
1. Describethedatadistribution.2. ComparedatadistributionsbetweenAndersonandWilliams.3. ComparedatadistributionsbetweenWilliamsandLemon.4. ComparedatadistributionsbetweenCroftandHurlea.5. ComparedatadistributionsbetweenJones,Spencer,andAnderson.6. ComparedatadistributionsbetweenSpencerandtheotherhistograms.7. Whichdistributionsaremostsimilar?Different?Explainyouranswer.
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SECONDARY MATH I // MODULE 3 MODELING DATA—9.2
Mathematics Vision Project Licensed under the Creative Commons Attribution CC BY 4.0 mathematicsvisionproject.org
DatasetI:Williams’sclass DatasetII:Lemon’sclass
DatasetIII:Croft’sClass DatasetIV:Anderson’sClass
DatasetV:Hurlea’sclass DatasetVI:Jones’class
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SECONDARY MATH I // MODULE 3 MODELING DATA—9.2
Mathematics Vision Project Licensed under the Creative Commons Attribution CC BY 4.0 mathematicsvisionproject.org
DatasetVII:Spencer’sclass
DatasetVIII:OverallAchievementTestScores
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SECONDARY MATH I // MODULE 3 MODELING DATA—9.2
Mathematics Vision Project Licensed under the Creative Commons Attribution CC BY 4.0 mathematicsvisionproject.org
9.2 Data Distribution – Teacher Notes A Practice Understanding Task Purpose:Studentsarealreadyfamiliarwithdotplots,boxplots,andhistograms.Thistaskhasthemdescribedatadistributionsandcompareshape,center,andspreadoftwoormoresetsofdata.
CoreStandardsFocus:
S.ID.2Usestatisticsappropriatetotheshapeofthedatadistributiontocomparecenter(median,mean)andspread(interquartilerange,standarddeviation)oftwoormoredifferentdatasets.S.ID.3Interpretdifferencesinshape,center,andspreadinthecontextofthedatasets,accountingforpossibleeffectsofextremedatapoints(outliers).
RelatedStandards:S.ID.1
StandardsforMathematicalPractice:
SMP3–Constructviableargumentsandcritiquethereasoningofothers
SMP4–Modelwithmathematics
SMP8–Lookforandexpressregularityinrepeatedreasoning
TheTeachingCycle:
Note:Itwouldbegoodtohavethedatayouwanttocompareinaformatthatislargeandvisibleforthewholegroupdiscussion.Forexample,youcouldcopythetwodatasetsyouwishtocompareandplacethemnexttoeachotherinaformatthatcanbeprojectedsothatwhenstudentsaresharingduringwholegroup,thevisualrepresentationisavailableforeveryonetosee.
Note:Studentshavebeenaskedtoidentifyandinterpretunivariatedatausingdotplots,histograms,andboxplotssincesixthgrade.Inthiscourse,studentsareaskedtocomparedatasetsusingtheirknowledgeofshape,center,andspreadandhavebecomemorecomfortablewiththeseattributes.Outliers,skeweddata,andnormaldistributionmaybenewthisyearaswell.Launch(WholeClass):
Havestudentsreadthevocabularytodescribedatadistributionsandaskthemtounderlineinformationthatisnewtothem.Havethemworkindividuallyforawhileonquestion1thathasthemdescribeeachdatasetbeforehavingthemworktogetherwithapartnerorsmallgrouptoanswertheremainingquestions(wheretheycomparedatasets).
SECONDARY MATH I // MODULE 3 MODELING DATA—9.2
Mathematics Vision Project Licensed under the Creative Commons Attribution CC BY 4.0 mathematicsvisionproject.org
Explore(SmallGroup):
Givestudentstimetoanswerthequestionscomparingdatasets.Listenforstudentstousevocabularyindescribingagivendataset,andtocompareshape,center,andspreadoftwoormoredatasets.Listenforstudentstocomparedatasets,notjustlistattributesofeach.Pressstudentstomakecomparisonsshowingtheyunderstandwhentousedatatodescribeandcompareshape,center,andspreadbetweendatasets.Examplesincludenoticingoutliers,variabilityandspreadbetweendata(noticethatHurleaandSpencerhaveascalethatisdifferentthantheothers),andothertrends.Again,makesurestudentsdonotjustlistcharacteristicsofeachdistributionandthinktheyare‘comparing’.Discuss(WholeClass):
Beginthewholegroupdiscussionbyselectingproblemsfromquestionsthatcomparedatasets.Basedonsmallgroupconversations,choosewhichcomparisonstoshareoutinwholegroup.Thefocusofthewholegroupdiscussionistodothefollowing:
o Showstudentunderstandingofusingstatisticsappropriatetotheshapeofthedatadistributiontocomparecenterandspread.
o Showstudentunderstandingofwhatinformationisprovidedwhengivenahistogram,boxplot,dotplot.
AlignedReady,Set,Go:ModelingData9.2
SECONDARY MATH I // MODULE 9
MODELING DATA – 9.2
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9.2
READY Topic:Drawingconclusionsfromdata.Inproblems1–4youaretoselectthebestanswerbasedonthegivendata.Belowyourchosenanswerisaconfidencescale.Circlethestatementthatbestdescribesyourconfidenceinthecorrectnessoftheansweryouchose.Thegoalistogainawarenessofhowitseemseasiertodrawconclusionsinsomecasesthaninothers. 1.Data:1,2,4,8,16,32, Thenextnumberinthelistwillbe:________
a.largerthan32 b.positive c.exactly64 d.lessthan32
IamcertainIamcorrect. Iamalittleunsure. IhadnoideasoIguessed.
Whataboutthedatamadeyoufeelthewayyoudidabouttheansweryoumarked?
2.Data:47,-13,-8,9,-23,14, Thenextnumberinthelistwillbe:________
a.positive b.negative c.lessthan100 d.lessthan-100
IamcertainIamcorrect. Iamalittleunsure. IhadnoideasoIguessed.
Whataboutthedatamadeyoufeelthewayyoudidabouttheansweryoumarked?
3.Data:-10,¾,38,-10,½,-81,-10,¼,93,-10, Thenextnumberinthelistwillbe:______
a.morethan93 b.negative c.afraction d.awholenumber
IamcertainIamcorrect. Iamalittleunsure. IhadnoideasoIguessed.
4.Data:50,-43,36,-29,22,-15 Thenextnumberinthelistwillbe:______
a.odd b.lessthan9 c.two-digits d.greaterthan-15
IamcertainIamcorrect. Iamalittleunsure. IhadnoideasoIguessed.
Whataboutthedatamadeyoufeelthewayyoudidabouttheansweryoumarked?
READY, SET, GO! Name PeriodDate
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SECONDARY MATH I // MODULE 9
MODELING DATA – 9.2
Mathematics Vision Project
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9.2
SET Topic:Creatinghistograms.
Mr.Austingaveaten-pointquiztohis9thgrademathclasses.Atotalof50studentstookthequiz.Mr.Austinscoredthequizzesandlistedthescoresalphabeticallyasfollows.
1stPeriodMath 2ndPeriodMath 3rdPeriodMath
6,4,5,7,5,
9,5,4,6,6,
8,5,7,5,8,
1,8,7,10,9
4,5,8,6,8,
9,5,8,5,1,
5,5,7,5,7
9,8,10,5,9,
7,8,9,8,5,
8,10,8,8,5
5.UseALLofthequizdatatomakeafrequencytablewithintervals.Useanintervalof2.
Score Frequency
0-1
2–3
4–5
6–7
8–9
10-11
6.Useyourfrequencytabletomakeahistogramforthedata
7.Describethedatadistributionofthehistogramyoucreated.Includewordssuchas:mode,skewed,outlier,normal,symmetric,center,andspread,iftheyapply.(Hint:Don’tforgetstandarddeviation.)
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SECONDARY MATH I // MODULE 9
MODELING DATA – 9.2
Mathematics Vision Project
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9.2
8.Createagraphofyourchoice(histogram,boxplot,dotplot)for1stand3rdperiod.
9.Whichclassperformedbetter? Justifyyouranswerbycomparingtheshape,center,andspreadofthetwoclasses.(Hint:Don’tforgetstandarddeviation.)
GO
Topic:Figuringpercentages
10.Whatpercentof97is11? 11.Whatpercentof88is132?
12.Whatpercentof84is9? 13.Whatpercentof88.6is70?
14.Whatis270%of60? 15.Whatis84%of25?
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