(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 7.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 283181, 5452] NotebookOptionsPosition[ 106505, 2781] NotebookOutlinePosition[ 275782, 5228] CellTagsIndexPosition[ 275702, 5223] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell["Organizing and Summarizing Data", "Title", CellChangeTimes->{{3.458426921828125*^9, 3.458426936015625*^9}}, FontFamily->"Arial", FontSize->48], Cell["Relative frequency charts", "Subtitle", FontFamily->"Arial", FontSize->36], Cell["Stan Markov", "TeacherName"], Cell["Business Statistics, 3rd period", "ClassName", CellChangeTimes->{{3.458426959140625*^9, 3.458426963421875*^9}}], Cell[CellGroupData[{ Cell["Lesson Overview", "Section"], Cell["\<\ Business Statistics, Introduction to Statistics, Introduction to Business\ \>", "Course", CellChangeTimes->{{3.458426970921875*^9, 3.45842699996875*^9}}], Cell["presentation 10 min, activity 20 min", "ActivityLength"], Cell["\<\ Grades 9-12: Data Analysis and Probability: Select and use appropriate \ statistical methods to analyze data Grades 9-12: Problem Solving: Build new mathematical knowledge through \ problem solving Grades 9-12: Problem Solving: Apply and adapt a variety of appropriate \ strategies to solve problems \ \>", "NCTMStandard", CellChangeTimes->{3.46040405140625*^9}], Cell["None", "Prerequisites", CellChangeTimes->{{3.459592220026265*^9, 3.4595922210106277`*^9}}], Cell["\<\ Students will learn to organize raw data into tables and graphs. \ \>", "Objectives", CellGroupingRules->{GroupTogetherGrouping, 10002.}, CellChangeTimes->{{3.458427014625*^9, 3.458427023984375*^9}, { 3.45842706425*^9, 3.458427087171875*^9}, {3.458427234359375*^9, 3.4584272574375*^9}}], Cell["demonstration, group project, or individual work", "ActivityType"], Cell["\<\ Michael Sullivan , Statistics: Informed Decisions Using Data, Third Edition, \ Prentice Hall, New Jersey, 2010\ \>", "ReferenceMaterial", CellChangeTimes->{{3.458427263359375*^9, 3.458427320734375*^9}, { 3.458427351046875*^9, 3.458427357953125*^9}}], Cell["", "Spacer", CellChangeTimes->{{3.458427390765625*^9, 3.4584274*^9}}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Goals", "Section", CellGroupingRules->{GroupTogetherGrouping, 10000.}, FontFamily->"Arial", FontSize->20], Cell["\<\ Students will be able to describe the steps needed to create a relative \ frequency plot.\ \>", "Item", CellGroupingRules->{GroupTogetherGrouping, 10000.}], Cell["\<\ Students will be able to create a relative frequency plot from data provided.\ \>", "Item", CellGroupingRules->{GroupTogetherGrouping, 10000.}] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell[CellGroupData[{ Cell["Instructor Presentation", "Section"], Cell[CellGroupData[{ Cell["Introduction", "Subsection"], Cell["\<\ When qualitative data is collected, we often want to determine how the \ individual data elements relate to one another and to the whole data set. \ This lesson plan outlines the process to turn raw data into information using \ a Relative Frequency Plot. 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But say someone asked you what percent of the \ therapy patients have shoulder problems.\ \>", "Text"], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"frequencytable", "=", RowBox[{"Tally", "[", "patients1", "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"fulldata", "=", RowBox[{"Prepend", "[", RowBox[{"frequencytable", ",", RowBox[{"{", RowBox[{"\"\\"", ",", "\"\\""}], "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"DisplayTable", "[", RowBox[{"fulldata", ",", RowBox[{ "TableLabel", "\[Rule]", "\"\\""}], ",", RowBox[{"ItemSize", "\[Rule]", "13"}]}], "]"}]}], "Input", CellChangeTimes->{{3.45842823653125*^9, 3.4584282651875*^9}, { 3.45842850215625*^9, 3.45842851053125*^9}, {3.4584820171643715`*^9, 3.4584820239458323`*^9}, {3.458482243874745*^9, 3.4584823041110473`*^9}, { 3.458482355987707*^9, 3.458482382191671*^9}, {3.4584830913731484`*^9, 3.4584831063724766`*^9}, {3.4584834694940844`*^9, 3.4584834852285194`*^9}, { 3.4586739643125*^9, 3.458674036515625*^9}, {3.4586740840625*^9, 3.458674096359375*^9}, {3.458674168828125*^9, 3.45867417615625*^9}, { 3.45867488296875*^9, 3.45867488415625*^9}, {3.45867495765625*^9, 3.45867496209375*^9}, {3.4589909719643555`*^9, 3.4589910154956055`*^9}}, FontSize->18], Cell[BoxData[ TemplateBox[{TagBox[ GridBox[{{"\"Body Part\"", "\"Number of Patients\""}, {"Back", "12"}, { "Wrist", "2"}, {"Elbow", "1"}, {"Hip", "2"}, {"Shoulder", "4"}, { "Knee", "5"}, {"Hand", "2"}, {"Groin", "1"}, {"Neck", "1"}}, AutoDelete -> False, BaseStyle -> {FontFamily -> "Helvetica", FontSize -> 18}, GridBoxAlignment -> {"Columns" -> {{Center}}}, GridBoxBackground -> {"Columns" -> {{ RGBColor[1, 1, 0.85]}}}, GridBoxFrame -> {"Columns" -> {{True}}, "Rows" -> {{True}}}, GridBoxItemSize -> {"Columns" -> {{13}}}, GridBoxSpacings -> {"Columns" -> {{2}}, "Rows" -> {{0.62}}}], "Grid"], StyleBox["\"Typical Physical Therapist's Day\"", StripOnInput -> False, FontFamily -> "Times", FontSize -> 16]}, "Labeled", DisplayFunction->(GridBox[{{ TagBox[ ItemBox[ PaneBox[ TagBox[#, "SkipImageSizeLevel"], Alignment -> {Center, Baseline}, BaselinePosition -> Baseline], DefaultBaseStyle -> "Labeled"], "SkipImageSizeLevel"]}, { ItemBox[#2, DefaultBaseStyle -> "LabeledLabel"]}}, GridBoxAlignment -> {"Columns" -> {{Center}}, "Rows" -> {{Center}}}, AutoDelete -> False, GridBoxItemSize -> {"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, BaselinePosition -> {1, 1}]& ), InterpretationFunction->(RowBox[{"Labeled", "[", RowBox[{#, ",", #2}], "]"}]& )]], "Output", CellChangeTimes->{3.460404280375*^9}, ShowStringCharacters->False, Background->None] }, {2}]], Cell["\<\ Well we could use the above table, but most business professionals prefer to \ see an additional column added to this table. The column is called Relative \ Frequency and it will help you estimate the number of shoulder patients that \ you typically see.\ \>", "Text", CellChangeTimes->{{3.458674378359375*^9, 3.458674416796875*^9}, { 3.458676283875*^9, 3.458676285421875*^9}, 3.45867810025*^9, { 3.45892374027912*^9, 3.45892375515412*^9}}], Cell["\<\ The Relative Frequency column is calculated in two steps. First, you add up \ the number of data elements in the data set. \ \>", "Text", CellChangeTimes->{{3.4584288031875*^9, 3.458428819109375*^9}, { 3.4584288556875*^9, 3.45842888225*^9}, {3.458429184953125*^9, 3.458429233359375*^9}, {3.45848167326523*^9, 3.4584818162842293`*^9}, { 3.458481894614359*^9, 3.458481946475062*^9}, {3.4584840200044117`*^9, 3.458484028207694*^9}, {3.458674410046875*^9, 3.458674413796875*^9}, 3.4586751015*^9}], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"dataelements", "=", RowBox[{"Length", "[", "patients1", "]"}]}]], "Input", CellChangeTimes->{{3.45842849675*^9, 3.458428498703125*^9}, { 3.4584818227218943`*^9, 3.458481857488409*^9}, {3.45867514684375*^9, 3.45867515103125*^9}}], Cell[BoxData["30"], "Output", CellChangeTimes->{{3.4584818593009553`*^9, 3.4584818730981836`*^9}, 3.4584822013265085`*^9, {3.458675152078125*^9, 3.45867515578125*^9}, 3.458678242609375*^9, 3.4589913305424805`*^9, 3.460404285828125*^9}] }, Open ]], Cell["\<\ Then you divide the number of specific data elements found in column two by \ the total number of data elements in the set. And Wa-La.\ \>", "Text", CellChangeTimes->{{3.458675106421875*^9, 3.458675120296875*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ StyleBox[ RowBox[{ RowBox[{"relfrequencytable", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"frequencytable", "[", RowBox[{"[", RowBox[{"n", ",", "1"}], "]"}], "]"}], ",", RowBox[{"frequencytable", "[", RowBox[{"[", RowBox[{"n", ",", "2"}], "]"}], "]"}], ",", RowBox[{"(", FractionBox[ RowBox[{"frequencytable", "[", RowBox[{"[", RowBox[{"n", ",", "2"}], "]"}], "]"}], "dataelements"], ")"}]}], "}"}], ",", RowBox[{"{", RowBox[{"n", ",", "1", ",", RowBox[{"Length", "[", "frequencytable", "]"}]}], "}"}]}], "]"}]}], ";"}], FontFamily->"Courier New", FontSize->10], "\[IndentingNewLine]", RowBox[{ RowBox[{"relfulldata", "=", StyleBox[ RowBox[{"Prepend", "[", RowBox[{"relfrequencytable", ",", RowBox[{"{", RowBox[{ "\"\\"", ",", "\"\\"", ",", "\"\\""}], "}"}]}], "]"}], FontSize->16]}], StyleBox[";", FontSize->16]}], "\[IndentingNewLine]", RowBox[{"DisplayTable", "[", RowBox[{"relfulldata", ",", RowBox[{ "TableLabel", "\[Rule]", "\"\\""}], ",", RowBox[{"ItemSize", "\[Rule]", "13"}]}], "]"}]}], "Input", CellChangeTimes->{{3.45842849675*^9, 3.458428498703125*^9}, { 3.4584818227218943`*^9, 3.458481857488409*^9}, {3.45848209669816*^9, 3.4584821834040594`*^9}, {3.458482216248861*^9, 3.4584822233897142`*^9}, { 3.458482586416109*^9, 3.4584826299088707`*^9}, {3.45848313498057*^9, 3.458483150651743*^9}, 3.4584833630097094`*^9, {3.4584834181972094`*^9, 3.4584834273222094`*^9}, {3.4584835132446823`*^9, 3.458483590824297*^9}, { 3.458483626715611*^9, 3.458483629106282*^9}, {3.458483673232129*^9, 3.4584838252819233`*^9}, {3.458674434203125*^9, 3.458674467203125*^9}, { 3.4586751290625*^9, 3.458675139421875*^9}, {3.45868007328125*^9, 3.458680085765625*^9}, {3.4589912680268555`*^9, 3.4589913244018555`*^9}}], Cell[BoxData[ TemplateBox[{TagBox[ GridBox[{{ "\"Body Part\"", "\"Number of Patients\"", "\"Relative Frequency\""}, { "Back", "12", FractionBox["2", "5"]}, {"Wrist", "2", FractionBox["1", "15"]}, {"Elbow", "1", FractionBox["1", "30"]}, {"Hip", "2", FractionBox["1", "15"]}, {"Shoulder", "4", FractionBox["2", "15"]}, {"Knee", "5", FractionBox["1", "6"]}, {"Hand", "2", FractionBox["1", "15"]}, {"Groin", "1", FractionBox["1", "30"]}, {"Neck", "1", FractionBox["1", "30"]}}, AutoDelete -> False, BaseStyle -> {FontFamily -> "Helvetica", FontSize -> 18}, GridBoxAlignment -> {"Columns" -> {{Center}}}, GridBoxBackground -> {"Columns" -> {{ RGBColor[1, 1, 0.85]}}}, GridBoxFrame -> {"Columns" -> {{True}}, "Rows" -> {{True}}}, GridBoxItemSize -> {"Columns" -> {{13}}}, GridBoxSpacings -> {"Columns" -> {{2}}, "Rows" -> {{0.62}}}], "Grid"], StyleBox["\"Typical Physical Therapist's Day\"", StripOnInput -> False, FontFamily -> "Times", FontSize -> 16]}, "Labeled", DisplayFunction->(GridBox[{{ TagBox[ ItemBox[ PaneBox[ TagBox[#, "SkipImageSizeLevel"], Alignment -> {Center, Baseline}, BaselinePosition -> Baseline], DefaultBaseStyle -> "Labeled"], "SkipImageSizeLevel"]}, { ItemBox[#2, DefaultBaseStyle -> "LabeledLabel"]}}, GridBoxAlignment -> {"Columns" -> {{Center}}, "Rows" -> {{Center}}}, AutoDelete -> False, GridBoxItemSize -> {"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, BaselinePosition -> {1, 1}]& ), InterpretationFunction->(RowBox[{"Labeled", "[", RowBox[{#, ",", #2}], "]"}]& )]], "Output", CellChangeTimes->{3.460404290609375*^9}, ShowStringCharacters->False, Background->None] }, {2}]], Cell[TextData[{ "This says that there is about a ", Cell[BoxData[ FormBox[ FractionBox["2", "5"], TraditionalForm]]], " chance that the next patient through the door has a back problem and there \ is only a ", Cell[BoxData[ FormBox[ FractionBox["1", "30"], TraditionalForm]]], " chance that the next patient has an elbow problem. (assuming the flow of \ past patients is an indicator of the flow of future patients). " }], "Text", CellChangeTimes->{{3.4584288031875*^9, 3.458428819109375*^9}, { 3.4584288556875*^9, 3.45842888225*^9}, {3.458429184953125*^9, 3.458429233359375*^9}, {3.45848167326523*^9, 3.4584818162842293`*^9}, { 3.458481894614359*^9, 3.458481946475062*^9}, {3.4584838837205453`*^9, 3.458483955893806*^9}, {3.4584840671146917`*^9, 3.4584841081937723`*^9}, 3.45867521771875*^9, {3.458680117890625*^9, 3.458680129921875*^9}, { 3.45868571384375*^9, 3.458685780234375*^9}}] }, Open ]], Cell[CellGroupData[{ Cell["", "SlideShowNavigationBar", CellTags->"SlideShowHeader"], Cell["\<\ Lets look at that table again. This time with the Relative Frequency stated \ as a decimal. \ \>", "Text", CellChangeTimes->{{3.458679665609375*^9, 3.45867967584375*^9}, { 3.458680301203125*^9, 3.4586803036875*^9}, {3.458680620296875*^9, 3.4586806329375*^9}, {3.458680675828125*^9, 3.45868072625*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"relfrequencytable", "=", RowBox[{"Table", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"frequencytable", "[", RowBox[{"[", RowBox[{"n", ",", "1"}], "]"}], "]"}], ",", RowBox[{"frequencytable", "[", RowBox[{"[", RowBox[{"n", ",", "2"}], "]"}], "]"}], ",", RowBox[{"N", "[", RowBox[{ RowBox[{"(", FractionBox[ RowBox[{"frequencytable", "[", RowBox[{"[", RowBox[{"n", ",", "2"}], "]"}], "]"}], "dataelements"], ")"}], ",", "2"}], "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"n", ",", "1", ",", RowBox[{"Length", "[", "frequencytable", "]"}]}], "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"relfulldata", "=", RowBox[{"Prepend", "[", 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