qu.1.topic=5 Number Summary@

qu.1.1.mode=Inline@
qu.1.1.name=01. Find the 5 Number Summary@
qu.1.1.comment=<p>First, rewrite the numbers in ascending order: $T</p>
<p>This makes the minimum and maximum easy to read.</p>
<p>There are an $ListParity number ($Num) of numbers, so the median is $Explain ($Median).</p>
<p>The first quartile is the median of the first $HalfNum numbers, while Q3 is the median of the top $HalfNum numbers.</p>@
qu.1.1.editing=useHTML@
qu.1.1.solution=@
qu.1.1.algorithm=$Q=1;
$Num=rint(6,16);
$Method=if(eq($Num/2,int($Num/2)),4,5);
$ListParity=if(eq($Method,4),"even","odd");
$Explain=if(eq($Method,4),"halfway between the middle two numbers","the middle number");
$HalfNum=int($Num/2);
$S=maple("randomize():
convert(LinearAlgebra[RandomVector]($Num,generator=rand(1..2*$Num)),list)");
$T=maple("sort($S)");
$PMedian=maple("Statistics[Median]($S)");
$Median=decimal(1,$PMedian);
$Min=min($S);
$Max=max($S);
$PQ1=maple("Statistics[Quartile]($S,1,method=$Method)");
$Q1=decimal(1,$PQ1);
$PQ3=maple("Statistics[Quartile]($S,3,method=$Method)");
$Q3=decimal(1,$PQ3);@
qu.1.1.uid=bae329fe-e3a2-4daf-b0d9-437141b34625@
qu.1.1.info=  Difficulty=2;
  Type=numeric;
  Course=202;
  Keyword=5 number summary;
@
qu.1.1.weighting=1,1,1,1,1@
qu.1.1.numbering=alpha@
qu.1.1.part.1.name=sro_id_1@
qu.1.1.part.1.answer.units=@
qu.1.1.part.1.numStyle=thousands scientific  arithmetic@
qu.1.1.part.1.editing=useHTML@
qu.1.1.part.1.showUnits=false@
qu.1.1.part.1.question=(Unset)@
qu.1.1.part.1.mode=Numeric@
qu.1.1.part.1.grading=exact_value@
qu.1.1.part.1.negStyle=minus@
qu.1.1.part.1.answer.num=$Q1@
qu.1.1.part.2.name=sro_id_2@
qu.1.1.part.2.answer.units=@
qu.1.1.part.2.numStyle=thousands scientific  arithmetic@
qu.1.1.part.2.editing=useHTML@
qu.1.1.part.2.showUnits=false@
qu.1.1.part.2.question=(Unset)@
qu.1.1.part.2.mode=Numeric@
qu.1.1.part.2.grading=exact_value@
qu.1.1.part.2.negStyle=minus@
qu.1.1.part.2.answer.num=$Median@
qu.1.1.part.3.name=sro_id_3@
qu.1.1.part.3.answer.units=@
qu.1.1.part.3.numStyle=thousands scientific  arithmetic@
qu.1.1.part.3.editing=useHTML@
qu.1.1.part.3.showUnits=false@
qu.1.1.part.3.question=(Unset)@
qu.1.1.part.3.mode=Numeric@
qu.1.1.part.3.grading=exact_value@
qu.1.1.part.3.negStyle=minus@
qu.1.1.part.3.answer.num=$Q3@
qu.1.1.part.4.name=sro_id_4@
qu.1.1.part.4.answer.units=@
qu.1.1.part.4.numStyle=thousands scientific  arithmetic@
qu.1.1.part.4.editing=useHTML@
qu.1.1.part.4.showUnits=false@
qu.1.1.part.4.question=(Unset)@
qu.1.1.part.4.mode=Numeric@
qu.1.1.part.4.grading=exact_value@
qu.1.1.part.4.negStyle=minus@
qu.1.1.part.4.answer.num=$Min@
qu.1.1.part.5.name=sro_id_5@
qu.1.1.part.5.answer.units=@
qu.1.1.part.5.numStyle=thousands scientific  arithmetic@
qu.1.1.part.5.editing=useHTML@
qu.1.1.part.5.showUnits=false@
qu.1.1.part.5.question=(Unset)@
qu.1.1.part.5.mode=Numeric@
qu.1.1.part.5.grading=exact_value@
qu.1.1.part.5.negStyle=minus@
qu.1.1.part.5.answer.num=$Max@
qu.1.1.question=<div title="University of Waterloo Statistics Bank/Numerical Analysis/Order Statistics/5 Number Summary/Q$Q">For the following set of data:<p>$S</p><p>Find:</p><p>a) The first quartile: <span>&nbsp;</span><1><span>&nbsp;</span></p><p>b) The median: <span>&nbsp;</span><2><span>&nbsp;</span></p><p>c) Third quartile: <span>&nbsp;</span><3><span>&nbsp;</span></p><p>d) Min: <span>&nbsp;</span><4><span>&nbsp;</span></p><p>e) Max: <span>&nbsp;</span><5></p></div>@

qu.2.topic=Quartiles@

qu.2.1.mode=Multiple Choice@
qu.2.1.name=01. Find quartiles@
qu.2.1.comment=<p>In this case our quartiles are the <u>average</u> of the surrounding numbers. So:</p>
<p><math xmlns='http://www.w3.org/1998/Math/MathML'><mstyle fontfamily='Times New Roman' mathsize='12' mathcolor='#000000'  veryverythinmathspace='0.0555556em' verythinmathspace='0.111111em' thinmathspace='0.166667em' mediummathspace='0.222222em' thickmathspace='0.277778em' verythickmathspace='0.333333em' veryverythickmathspace='0.388889em' scriptlevel='0' scriptsizemultiplier='0.71' scriptminsize='8.0pt'><mrow><msub><mi>Q</mi><mrow><mn>1</mn></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><mi mathvariant='normal'>$X1</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$X2</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi mathvariant='normal'>$Q1</mi><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mspace height='0.0ex' width='0.0em' depth='0.0ex' linebreak='newline'/><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><msub><mi>Q</mi><mrow><mn>2</mn></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><mi mathvariant='normal'>$X2</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$X3</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi mathvariant='normal'>$Q2</mi><mo separator='true' lspace='0.0em' rspace='0.3333333em'>&comma;</mo><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><mspace height='0.0ex' width='0.0em' depth='0.0ex' linebreak='newline'/><mo lspace='0.0em' rspace='0.0em'>&#32;</mo><msub><mi>Q</mi><mrow><mn>3</mn></mrow></msub><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mfrac><mrow><mi mathvariant='normal'>$X3</mi><mo lspace='0.2222222em' rspace='0.2222222em'>&plus;</mo><mi mathvariant='normal'>$X4</mi></mrow><mrow><mn>2</mn></mrow></mfrac><mo lspace='0.2777778em' rspace='0.2777778em'>&equals;</mo><mi mathvariant='normal'>$Q3</mi></mrow></mstyle></math></p>@
qu.2.1.editing=useHTML@
qu.2.1.solution=@
qu.2.1.algorithm=$Q=1;
$X1=range(5,14);
$X2=range($X1+4,$X1+11);
$X3=range($X2+4,$X2+11);
$X4=range($X3+4,$X3+11);
$Q1=($X1+$X2)/2;
$Q2=($X2+$X3)/2;
$Q3=($X3+$X4)/2;@
qu.2.1.uid=4d043096-c271-402c-aad3-56fc01572202@
qu.2.1.info=  Difficulty=3;
  Keyword=quartile;
  Course=202;
@
qu.2.1.question=<div title="University of Waterloo Statistics Bank/Numerical Analysis/Order Statistics/Quartiles/Q$Q">Find Q<sub>1</sub> , Q<sub>2</sub> , and Q<sub>3</sub> for the following data set:&nbsp; $X1, $X2, $X3, $X4</div>@
qu.2.1.answer=1@
qu.2.1.choice.1=Q<sub>1</sub> = $Q1 , Q<sub>2</sub> = $Q2 , and Q<sub>3</sub> = $Q3@
qu.2.1.choice.2=Q<sub>1</sub> = $Q1 , Q<sub>2</sub> = $X3 , and Q<sub>3</sub> = $X4@
qu.2.1.choice.3=Q<sub>1</sub> = $X1 , Q<sub>2</sub> = $Q2 , and Q<sub>3</sub> = $X4@
qu.2.1.choice.4=Q<sub>1</sub> = $Q3 , Q<sub>2</sub> = $Q2 , and Q<sub>3</sub> = $Q1@
qu.2.1.fixed=@

