C1:U2:L2:Investigation1:MeasuringPosition
Ifyouareatthe40thpercentileofheightforyourage,thatmeansthat40%ofpeopleyourage,thatmeans
that40%ofpeopleyourageareyourheightorshorterthanyouare60%aretaller.Percentiles,likethe
median,describethepositionofavalueinadistribution.Yourworkinthisinvestigationwillhelpyouanswer
thisquestion:
1. Howdoyoufindandinterpretpercentilesandquartiles?
Thephysicalgrowthchartsbelowdisplaytwosetsofcurvedlines.Thecurvedlinesatthetopgiveheight
percentiles,whilethecurvedlinesatthebottomgiveweightpercentile.Thepercentilesarethesmall
numbers5,10,25,50,75,90,and95ontherightendsofthecurvedlines.
1. SupposeJohnisa14-year-oldboywhoweighs45kg(100pounds).Johnisatthe25thpercentileof
weightforhisage.Twenty-fivepercentof14–year-oldboysweighthesameoflessthanJohnand75%
weightmorethanJohn.IfJohn’sheightis170cm(almost5’7”),heisatthe75thpercentileofheight
forhisage.BasedontheinformationgivenaboutJohn,howwouldyoudescribeJohn’sgeneral
appearance?
2. Growthchartscontainanamazingamountofinformation.Usethegrowthchartstohelpyouanswer
thefollowingquestions.
a. Whatistheapproximatepercentilefora9-year-oldgirlwhois128cmtall?
b. Whatisthe25thpercentileofheightfor4-year-oldboys?The50thpercentile?The75th
percentile?
c. Abouthowtalldoesa12-year-oldgirlhavetobesothatsheisastallortallerthan75%ofthe
girlsherage?Howtalldoesa12-year-oldboyhavetobe?
d. Howtallwoulda14-year-oldboyhavetobesothatyouwouldconsiderhim“tall”forhisage?
Howdidyoumakethisdecision?
e. Accordingtothechart,istheremorevariabilityintheheightsof2-year-oldgirlsor14-year-old
girls?
f. Howcanyoutellfromtheheightandweightchartwhenchildrenaregrowingthefastest?
Whenistheincreaseinweightthegreatestforgirls?Forboys?
3. Somepercentileshavespecialnames.The25thpercentileiscalledthelowerorfirstquartile.The75th
percentileiscalledtheupperorthirdquartile.Findtheheightsof6-year-oldgirlsonthegrowth
charts.
a. Estimatetheinterpretthelowerquartile.
b. Estimateandinterprettheupperquartile.
c. Whatwouldthemiddleorsecondquartilebecalled?Whatisitspercentile?
4. Thehistogrambelowdisplaystheresultsofasurveyfilledoutby460varsityathletesinfootballand
women’sandmen’sbasketballfromschoolsaroundDetroit,MI.Theseresultswerereportedina
schoolnewspaper.
a. Whatisanunusualfeatureofthisdistribution?Whatdoyouthinkisthereasonforthis?
b. Estimatethemedianandthequartiles.Usetheupperquartileinasentencethatdescribesthis
distribution.
c. Estimatethepercentileforanathletewhostudied3.5hours.
5. Supposeyouget40pointsoutof50onyournextmathtest.Canyoudetermineyourpercentage
correct?Yourpercentileinyourclass?Ifso,calculatethem.Ifnot,explainwhynot.
6. Themathhomeworkgradesfortwoninth-gradestudentsatLakeviewHighSchoolaregiven.
a. Whichofthestudentshasgreatervariabilityinhisorhergrades?
b. Putthe20gradesforSusaninanorderedlistandfindthemedian.
i. Findthequartilesbyfindingthemediansofthelowerandupperhalves.
ii. Markthepositionsofthemedianandquartilesonyourorderedlistofgrades.
c. Jackhas19grades.Puttheminanorderedlistandfindthemedian.
i. Tofindthefirstandthirdquartileswhenthereareanoddnumberofvalues,one
strategyistoleaveoutthemedianandthenfindthemedianofthelowervaluesandthe
medianoftheuppervalues.UsethisstrategytofindthequartilesofJack’sgrades.
ii. MarkthepositionsofthemedianandquartilesonyourorderedlistofJack’sgrades.
d. Forwhichstudentarethelowerandupperquartilesfurtherapart?Whatdoesthistellyou
aboutthevariabilityofthegradesofthetwostudents?