Copyright©AndrewChambers(2021).Allrightsreserved.

Boxandwhisker,Cumulativefrequency,Standarddeviation

Name……………………………

(1) Thescoresthatstudentsgetonatestoutof15arerecordedinaboxandwhiskerplotshownbelow:

(a) Findtheinterquartilerange(b) Whatpercentageofstudentsgotlessthan8marks?(c) Ascoregreaterthankwouldbeclassifiedasanoutlier.Findk.Explainwhytherecan

benooutliersforthisdata.(2) Thenumberofcupsofcoffeestudentsdrinkeachweekisrecordedbelow:

0,0,1,1,1,2,2,2,2,3,3,4,5,8,12,15

(a) Findthemedian,lowerquartile,upperquartileandinterquartilerange.(b) Findthestandarddeviation.(c) Findanyoutliersforthisdata.(d) Drawtheboxandwhiskerplotofthisdata:

Copyright©AndrewChambers(2021).Allrightsreserved.

(3) Asurveyofteachers’sleepobtainedthefollowingresults:

Hours sleep 0 ≤ ℎ < 5 5 ≤ ℎ < 7 7 ≤ ℎ < 9 9 ≤ ℎ < 11 Frequency 2 9 12 2

(a) Findanestimationforthemean.(b) Drawacumulativefrequencycurveonthegraphbelow.

(c) Findthemedianandinterquartilerangefromyourcurve.(ii) Approximatelywhatpercentageofteachersgotmorethan8hourssleep?(d) Iftheteacherwiththeleasthourssleephad4hourssleeptherangewas6hours,

sketchaboxandwhiskerplotbeneathyourcumulativefrequencycurve.

Copyright©AndrewChambers(2021).Allrightsreserved.

(4) Agardenercollects2differenttypesofleaves(AandB)intheirgardenandnotestheirwidths.Shethendrawsthefollowingboxandwhiskerplots:

(a) Withreferencetoboththemedianandinterquartilerangecomparethetwodistributions.

(b) Whichtypeofleafwidthcouldbenormallydistributed?Explainyouranswer.(5) Studentsareaskedaboutthenumberofbrothersandsistersthattheyhave.The

resultsarerecordedbelow:

Number of siblings 0 1 2 3 4 Frequency 8 12 15 5 2

(a) Findthestandarddeviation.(b) Findthemean.(c) Whatpercentageofstudents’answersarewithinonestandarddeviationofthemean?

Copyright©AndrewChambers(2021).Allrightsreserved.

(6) Agroupofofficeworkersaregivenatasktocompleteandthetimetakenisrecorded.

(a) Findanestimationforthemeannumberofminutestaken.(b) Usethedatamidpointstofindanestimationforthestandarddeviation.(c) Anyworkerwhowasmorethan2standarddeviationsabovethemeanhastoattend

anextraweekendtrainingsession.Workerstakinglongerthanwhattimewillhavetoattend?

(7) Studentsaregivenamathstestinwhichtheaveragescoreis65marksandthe

standarddeviationis18.(a) Theteacherdecidesthattheyhavemarkedtooharshlyanddecidestoincrease

everyone’sscoreby5marks.Findthenewmeanandstandarddeviation.(b) Theteacherdecidestoincreaseeveryone’soriginalscoresby5%.Findthenewmean

andstandarddeviation.