(*********************************************************************** Mathematica-Compatible Notebook This notebook can be used on any computer system with Mathematica 3.0, MathReader 3.0, or any compatible application. The data for the notebook starts with the line of stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). NOTE: If you modify the data for this notebook not in a Mathematica- compatible application, you must delete the line below containing the word CacheID, otherwise Mathematica-compatible applications may try to use invalid cache data. For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 21031, 710]*) (*NotebookOutlinePosition[ 22086, 746]*) (* CellTagsIndexPosition[ 22042, 742]*) (*WindowFrame->Normal*) Notebook[{ Cell[TextData[{ StyleBox["Miniproject\nFor The\n", Evaluatable->False, TextAlignment->Center, AspectRatioFixed->True, FontFamily->"New York", FontSize->24], StyleBox["Mathematica", Evaluatable->False, TextAlignment->Center, AspectRatioFixed->True, FontFamily->"New York", FontSize->24, FontSlant->"Italic"], StyleBox[" Workshop\n\n\n", Evaluatable->False, TextAlignment->Center, AspectRatioFixed->True, FontFamily->"New York", FontSize->24] }], "Text", Evaluatable->False, TextAlignment->Center, AspectRatioFixed->True], Cell[GraphicsData["PICT", "\<\ 0ll1e01E0Y@1LQ41X022X02>0@0:000000;@0T2H02H1e01@0RX1N07D05D2:P5b 0M@0E@8Z0G800@;K00;K00;K00;K00;K00;K00;K00;K00;K00;K00;K00;K00;K 00;K00;K00;K00;K00;K00;K00;K00;K00;K00;K00;K00;K00;K00;K00;K00;K 00;K00;K00;K00;K00;K00;K00;K00;K00;K00;K00;K00;K00;K00;K00;K00;K 00;K00;K00;K00;K00;K00;K00;K00;K00;K00;K00;K00;K00;K00;K00;K00;K 00;K00;K00;K00;K00;K00;K00;K00;K00;K00;K00;K00;K00;K00;K00;K00;K 00;K00;K00;K00;K00;K00;K00;K00;K00;K09P09P8Z0502P05h0RX0E@:00G82 :P1E0X01LP010]/00]/00]/00]/00]/00]/00]/00]/00]/00]/00]/00]/00]/0 0]/00]/00]/00]/00]/00]/00]/00]/00]/00]/00]/00]/00]/00]/00]/00]/0 0]/00]/00]/00]/00]/00]/00]/00]/00]/00]/00]/00]/00]/00]/00]/00]/0 0]/00]/00]/00]/00]/00]/00]/00]/00]/00]/00]/00]/00]/00]/00]/00]/0 0]/00]/00]/00]/00]/00]/00]/00]/00]/00]/00]/00]/00]/00]/00]/00]/0 0]/00]/00]/00]/00]/00]/00]/00]/00]/0V00V0X00D0:D0GP2P01E0Y@1LP:0 05D2U05b0042f`02f`02f`02f`02f`02f`02f`02f`02f`02f`02f`02f`02f`02 f`02f`02f`02f`02f`02f`02f`2P08l700800S01fP1K0WT1EC01k`1b0Xh1K:40 UP061P000080X@2J00Sonh0003F00:00V0<00`@13@0>:08A0:`=D6USM7EbIB15 LW9_LZ00VJ00Uj40UP061P000080X@2J00P04`0004X00:00V0@23@0<:08[09LH E6QULVDPJG"], "Graphics", Evaluatable->False, AspectRatioFixed->True, ImageSize->{378, 111}, ImageMargins->{{19, Inherited}, {Inherited, 2}}], Cell[TextData["\n\n\n\n\n\n"], "Input", AspectRatioFixed->True], Cell[TextData[{ StyleBox["Carol Castellon", Evaluatable->False, AspectRatioFixed->True, FontSize->14], StyleBox["", Evaluatable->False, AspectRatioFixed->True] }], "Subsection", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ StyleBox["Descriptive Statistics", Evaluatable->False, AspectRatioFixed->True, FontSize->14], StyleBox["", Evaluatable->False, AspectRatioFixed->True] }], "Subsection", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{Cell[TextData[{ StyleBox["Brief Description\n", Evaluatable->False, AspectRatioFixed->True, FontSize->14], StyleBox[ " This project is an illustration of the built-in functions of the \ Descriptive Statistics package. This package is automatically loaded when \ most other statistical packages are used.\n This project also provides an \ explaination of the measures used in descriptive statistics. ", Evaluatable->False, AspectRatioFixed->True] }], "Subsection", Evaluatable->False, AspectRatioFixed->True], Cell[TextData["\n\n\n\n\n\n\n\n\n\n\n\n"], "Input", AspectRatioFixed->True]}, Open]], Cell[CellGroupData[{Cell[TextData["Descriptive Statistics"], "Title", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{Cell[TextData["Initialization:"], "SmallText", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "<True, AspectRatioFixed->True]}, Open]], Cell[CellGroupData[{Cell[TextData["1. Averages"], "Section", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ StyleBox["Given a set of ranked data, the ", Evaluatable->False, AspectRatioFixed->True, FontColor->RGBColor[0, 0, 1]], StyleBox["median", Evaluatable->False, AspectRatioFixed->True, FontWeight->"Bold", FontColor->RGBColor[1, 0, 1]], StyleBox[ " is the number which splits the data into equal halves.\nExample: Given \ the set of data: 3,2,7,6,3,10,8\nFirst rank the data, then locate the \ median.", Evaluatable->False, AspectRatioFixed->True, FontColor->RGBColor[0, 0, 1]] }], "Text", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{Cell[TextData[ "data1 := {3,2,7,6,3,10,8}\nsrtdata1 = Sort[data1]\nMedian[data1]"], "Input", AspectRatioFixed->True], Cell[OutputFormData["\<\ {2, 3, 3, 6, 7, 8, 10}\ \>", "\<\ {2, 3, 3, 6, 7, 8, 10}\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True], Cell[OutputFormData["\<\ 6\ \>", "\<\ 6\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True]}, Open]], Cell[TextData[ "There were 7 peices of data in the set. If there are an even number of \ pieces of data, the median may not necessarily be a member of the data set.\n\ For example:\t\t3,2,7,6,9,8"], "Text", Evaluatable->False, AspectRatioFixed->True, FontColor->RGBColor[0, 0, 1]], Cell[CellGroupData[{Cell[TextData[ "data2 := {3,2,7,6,9,8}\nSort[data2]\nN[Median[data2]]"], "Input", AspectRatioFixed->True], Cell[OutputFormData["\<\ {2, 3, 6, 7, 8, 9}\ \>", "\<\ {2, 3, 6, 7, 8, 9}\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True], Cell[OutputFormData["\<\ 6.5\ \>", "\<\ 6.5\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True]}, Open]], Cell[TextData[ "You can see that the median, 6\[Trademark]\[IAcute]\:2215 , is not a member \ of the data set, yet it divides the set into two equal halves."], "Text", Evaluatable->False, AspectRatioFixed->True, FontColor->RGBColor[0, 0, 1]], Cell[TextData[{ StyleBox["\nThe arithmetic ", Evaluatable->False, AspectRatioFixed->True, FontColor->RGBColor[0, 0, 1]], StyleBox["mean", Evaluatable->False, AspectRatioFixed->True, FontWeight->"Bold", FontColor->RGBColor[1, 0, 1]], StyleBox[ " is the only average which uses all the values of a data set. It is \ called the \"", Evaluatable->False, AspectRatioFixed->True, FontColor->RGBColor[0, 0, 1]], StyleBox["balance point", Evaluatable->False, AspectRatioFixed->True, FontWeight->"Bold", FontColor->RGBColor[0, 0, 1]], StyleBox[ "\" of a distribution because the sum of the deviations to the left of the \ mean equals the sum of the deviations to the right of the mean.\nTo find the \ mean, all the data values are added, and then divided by the number of pieces \ of data (sample size).\nIn symbols: ", Evaluatable->False, AspectRatioFixed->True, FontColor->RGBColor[0, 0, 1]], StyleBox["\[LongDash]x", Evaluatable->False, AspectRatioFixed->True, FontColor->RGBColor[0, 0, 1], FontVariations->{"StrikeThrough"->True}], StyleBox[ " = \[AGrave]\[DownExclamation]\:02dc x\[CapitalDelta] \[Divide]", Evaluatable->False, AspectRatioFixed->True, FontColor->RGBColor[0, 0, 1]], StyleBox["\[Divide]", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Geneva", FontColor->RGBColor[0, 0, 1]], StyleBox[" n\nExample: Given the data set: 2,3,6,7,8,10\nThe mean is", Evaluatable->False, AspectRatioFixed->True, FontColor->RGBColor[0, 0, 1]] }], "Text", Evaluatable->False, AspectRatioFixed->True, FontColor->RGBColor[0, 0, 1]], Cell[CellGroupData[{Cell[TextData["N[Mean[data1]]"], "Input", AspectRatioFixed->True], Cell[OutputFormData["\<\ 5.571428571428571428\ \>", "\<\ 5.57143\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True]}, Open]], Cell[TextData[ "There are other kinds of means.\nThe Geometric mean and Harmonic mean, \ respectively, are"], "SmallText", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{Cell[TextData["N[GeometricMean[data1]]\nN[HarmonicMean[data1]]"], "Input", AspectRatioFixed->True], Cell[OutputFormData["\<\ 4.820447946454280469\ \>", "\<\ 4.82045\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True], Cell[OutputFormData["\<\ 4.11476557032890133\ \>", "\<\ 4.11477\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True]}, Open]], Cell[TextData[{ StyleBox["\nThe", Evaluatable->False, AspectRatioFixed->True], StyleBox[" mode", Evaluatable->False, AspectRatioFixed->True, FontWeight->"Bold", FontColor->RGBColor[1, 0, 1]], StyleBox[ " is the peice of data with the highest frequency in the set of data.\n\ Example: Given the set of data: 3,2,7,6,3,10,8\nThe mode is", Evaluatable->False, AspectRatioFixed->True] }], "SmallText", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{Cell[TextData["Mode[data1]"], "Input", AspectRatioFixed->True], Cell[OutputFormData["\<\ 3\ \>", "\<\ 3\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True]}, Open]], Cell[TextData[{ StyleBox["\nOther measures of central tendancy include the ", Evaluatable->False, AspectRatioFixed->True], StyleBox["midhinge", Evaluatable->False, AspectRatioFixed->True, FontWeight->"Bold", FontColor->RGBColor[1, 0, 1]], StyleBox[" (also called the midquartile) and the ", Evaluatable->False, AspectRatioFixed->True], StyleBox["midrange", Evaluatable->False, AspectRatioFixed->True, FontWeight->"Bold", FontColor->RGBColor[1, 0, 1]], StyleBox[ ".\nExample: Given the set of data: 3,2,7,6,3,10,8\nThe midhinge and \ midrange, respectively, are", Evaluatable->False, AspectRatioFixed->True] }], "SmallText", Evaluatable->False, AspectRatioFixed->True], Cell[CellGroupData[{Cell[TextData[ "midhinge = (N[Quantile[data1,.25]] + \n N[Quantile[data1,.75]])/2 \ \nmidrange = N[(First[srtdata1] + Last[srtdata1])/2]"], "Input", AspectRatioFixed->True], Cell[OutputFormData["\<\ 5.5\ \>", "\<\ 5.5\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True], Cell[OutputFormData["\<\ 6.\ \>", "\<\ 6.\ \>"], "Output", Evaluatable->False, AspectRatioFixed->True]}, Open]], Cell[TextData[{ StyleBox["Note: A general command, LocationReport[", Evaluatable->False, AspectRatioFixed->True], StyleBox["data", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox["] , gives the mean, harmonic mean and median with one input.\n", Evaluatable->False, AspectRatioFixed->True] }], "SmallText", Evaluatable->False, AspectRatioFixed->True]}, Open]], Cell[CellGroupData[{Cell[TextData["2.\t Dispersion"], "Section", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ StyleBox[ "There are several measures which describe how the data is dispersed.\n\n\ The simplest is the ", Evaluatable->False, AspectRatioFixed->True], StyleBox["range", Evaluatable->False, AspectRatioFixed->True, FontWeight->"Bold", FontColor->RGBColor[1, 0, 1]], StyleBox[ ", the distance between the highest and lowest data value; i.e. Range = H - \ L\nExample: Given the set of data: 3,2,7,6,3,10,8\nThe range is:", Evaluatable->False, AspectRatioFixed->True] }], "SmallText", Evaluatable->False, AspectRatioFixed->True], Cell[TextData["data1 := {3,2,7,6,3,10,8}\nSampleRange[data1]"], "Input", AspectRatioFixed->True], Cell[TextData[{ StyleBox["Interquartile range", Evaluatable->False, AspectRatioFixed->True, FontWeight->"Bold", FontColor->RGBColor[1, 0, 1]], StyleBox[ " can also be found; i.e., IQ Range = Q\[Sterling] - Q\[DownExclamation] \ \nThe interquartile range is: ", Evaluatable->False, AspectRatioFixed->True] }], "SmallText", Evaluatable->False, AspectRatioFixed->True], Cell[TextData["N[InterquartileRange[data1]]"], "Input", AspectRatioFixed->True], Cell[TextData[{ StyleBox["\nThe two measures of variation most widely used are ", Evaluatable->False, AspectRatioFixed->True], StyleBox["variance", Evaluatable->False, AspectRatioFixed->True, FontWeight->"Bold", FontColor->RGBColor[1, 0, 1]], StyleBox[" and ", Evaluatable->False, AspectRatioFixed->True], StyleBox["standared deviation", Evaluatable->False, AspectRatioFixed->True, FontWeight->"Bold", FontColor->RGBColor[1, 0, 1]], StyleBox[ ". (The package uses unbiased variance)\nThe Variance = s\[Currency] = \ \[Mu]\[IAcute]\[Mu]\:2215 \[AGrave]\[CapitalDelta] (x\[CapitalDelta] - ", Evaluatable->False, AspectRatioFixed->True], StyleBox["\[LongDash]x", Evaluatable->False, AspectRatioFixed->True, FontVariations->{"StrikeThrough"->True}], StyleBox[" )\[Currency] where m = n-1 is:", Evaluatable->False, AspectRatioFixed->True] }], "SmallText", Evaluatable->False, AspectRatioFixed->True], Cell[TextData["N[Variance[data1]]"], "Input", AspectRatioFixed->True], Cell[TextData[{ StyleBox["\nThe Standard Deviation = s = ", Evaluatable->False, AspectRatioFixed->True], StyleBox["\[Sqrt]", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Geneva"], StyleBox[" s\[Currency] ", Evaluatable->False, AspectRatioFixed->True] }], "SmallText", Evaluatable->False, AspectRatioFixed->True], Cell[TextData["N[StandardDeviation[data1]]"], "Input", AspectRatioFixed->True], Cell[TextData[{ StyleBox[ "Although there are other measures of dispersion, only the simplest were \ presented here.\nNote: A general command, DispersionReport[", Evaluatable->False, AspectRatioFixed->True], StyleBox["data", Evaluatable->False, AspectRatioFixed->True, FontSlant->"Italic"], StyleBox[ "], gives the variance, standard deviation, sample range, mean deviation, \ median deviation, and quartile deviation with one input.\n\n", Evaluatable->False, AspectRatioFixed->True] }], "SmallText", Evaluatable->False, AspectRatioFixed->True]}, Open]], Cell[CellGroupData[{Cell[TextData["3.\t Position"], "Section", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[{ StyleBox[ "Statisticians are often interested in location of selected pieces of data.\ \nThe most common measures of postion are Percentiles, Quartiles, and \ Deciles.\n\n", Evaluatable->False, AspectRatioFixed->True], StyleBox["Quartiles", Evaluatable->False, AspectRatioFixed->True, FontWeight->"Bold", FontColor->RGBColor[1, 0, 1]], StyleBox[ " divide the ranked data set into 4 parts. Therefore, there are only 3 \ quartiles.\nExample: Given the set of data: 3,2,7,6,3,10,8,5\nThe Quartiles \ for the ranked data are", Evaluatable->False, AspectRatioFixed->True] }], "SmallText", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "data1 := {3,2,7,6,3,10,8,5}\nsrtdata1 = Sort[data1]\nN[Quartiles[data1]]"], "Input", AspectRatioFixed->True], Cell[TextData[{ StyleBox["Percentiles", Evaluatable->False, AspectRatioFixed->True, FontWeight->"Bold", FontColor->RGBColor[1, 0, 1]], StyleBox[ " divide the ranked data set into 100 parts. Therefore, there are only 99 \ percentiles. When a set of data has only 8 pieces, it is obvious that to \ divide it into 100 parts, a single data value must \"share\" the name of many \ percentiles. For example, the data value 3 in the data set, is the 13th \ through the 37th percentiles.\nTo find the value of a percentile, multiply: \ % \[CapitalEAcute] n\nThen, If this answer is not whole, round up; if this \ anwer is whole, add \[Trademark]\[IAcute]\[Trademark]\:2215 . Use this \ result as a locator of the desired percentile.\nFor example, in the given set \ of data, the 35th percentile is:", Evaluatable->False, AspectRatioFixed->True] }], "SmallText", Evaluatable->False, AspectRatioFixed->True], Cell[TextData["N[Quantile[data1,.35]]"], "Input", AspectRatioFixed->True], Cell[TextData["The 80th percentile is:"], "SmallText", Evaluatable->False, AspectRatioFixed->True], Cell[TextData["N[Quantile[data1,.80]]"], "Input", AspectRatioFixed->True], Cell[TextData[{ StyleBox["Deciles", Evaluatable->False, AspectRatioFixed->True, FontWeight->"Bold", FontColor->RGBColor[1, 0, 1]], StyleBox[ " divide the ranked data set into 10 parts. Therefore, there are only 9 \ deciles. Deciles are found via percentiles.\nThe 4th Decile is", Evaluatable->False, AspectRatioFixed->True] }], "SmallText", Evaluatable->False, AspectRatioFixed->True], Cell[TextData["N[Quantile[data1,.40]]"], "Input", AspectRatioFixed->True], Cell[TextData[{ StyleBox[ "\nAnother measure which describes the location of a particular piece of \ data is the ", Evaluatable->False, AspectRatioFixed->True], StyleBox["z-score", Evaluatable->False, AspectRatioFixed->True, FontWeight->"Bold", FontColor->RGBColor[1, 0, 1]], StyleBox[ ", or standard score. The z-score tells where the data is located relative \ to the mean, in terms of the number of standard deviations away from the \ mean. A z-score of 1.5 would say that the data is located 1.5 standard \ deviations to the right of the mean. \nThe formula to find a z-score is: z\ \[CapitalDelta] = (x\[CapitalDelta] - ", Evaluatable->False, AspectRatioFixed->True], StyleBox["\[LongDash]x", Evaluatable->False, AspectRatioFixed->True, FontVariations->{"StrikeThrough"->True}], StyleBox[" ) ", Evaluatable->False, AspectRatioFixed->True], StyleBox["\[Divide] s", Evaluatable->False, AspectRatioFixed->True, FontFamily->"Geneva"], StyleBox[ "\nExample: Given the set of data: 3,2,7,6,3,10,8,5\nThe z-score for the \ data value 6 is", Evaluatable->False, AspectRatioFixed->True] }], "SmallText", Evaluatable->False, AspectRatioFixed->True], Cell[TextData["z = N[(6 - Mean[data1])/StandardDeviation[data1]]"], "Input", AspectRatioFixed->True], Cell[TextData[ "This says that the piece of data, 6, is located 0.18 standard deviations to \ the right of the mean."], "SmallText", Evaluatable->False, AspectRatioFixed->True]}, Open]], Cell[CellGroupData[{Cell[TextData["4.\t\tGraphs and Charts"], "Section", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "To produce bar graphs and circle graphs, you need to use the Graphics \ package.\n\nUsing an arbitrary set of data which simulates a set of Quiz \ scores,"], "SmallText", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "data = {5,7,8,9,8,8,10,6,7,10,4,8,10,9,9,7,9,8}\nfdata := \ Frequencies[data]"], "Input", AspectRatioFixed->True], Cell[TextData["The bar graph of the data set looks like this."], "SmallText", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "BarChart[fdata,PlotLabel->\"Frequency of Quiz Scores\"];"], "Input", AspectRatioFixed->True], Cell[TextData[ "The pie graph of the data set can be customized to seperate out any subset \ of scores. "], "SmallText", Evaluatable->False, AspectRatioFixed->True], Cell[TextData[ "DisplayTogetherArray[PieChart[fdata],\n\t\ PieChart[fdata,PieExploded->{{1,.3},{2,.3}}]];"], "Input", AspectRatioFixed->True]}, Open]]}, Open]] }, FrontEndVersion->"Macintosh 3.0", ScreenRectangle->{{0, 640}, {0, 460}}, WindowToolbars->{}, CellGrouping->Manual, WindowSize->{520, 365}, WindowMargins->{{28, Automatic}, {Automatic, 16}}, PrivateNotebookOptions->{"ColorPalette"->{RGBColor, -1}}, ShowCellLabel->True, ShowCellTags->False, RenderingOptions->{"ObjectDithering"->True, "RasterDithering"->False}, MacintoshSystemPageSetup->"\<\ AVU/IFiQKFD000000V:^/09R]g0000000OVaH097bCP0AP1Y06`0I@1^0642HZj` 0V:gT0000001nK500TO9>000000000000000009R[[0000000000000000000000 00000000000000000000000000000000\>" ] (*********************************************************************** Cached data follows. If you edit this Notebook file directly, not using Mathematica, you must remove the line containing CacheID at the top of the file. The cache data will then be recreated when you save this file from within Mathematica. ***********************************************************************) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[1711, 51, 595, 23, 70, "Text", Evaluatable->False], Cell[2309, 76, 1492, 25, 70, 1368, 21, "GraphicsData", "PICT", "Graphics", Evaluatable->False], Cell[3804, 103, 65, 1, 70, "Input"], Cell[3872, 106, 249, 10, 70, "Subsection", Evaluatable->False], Cell[4124, 118, 256, 10, 70, "Subsection", Evaluatable->False], Cell[CellGroupData[{ Cell[4403, 130, 548, 14, 70, "Subsection", Evaluatable->False], Cell[4954, 146, 77, 1, 70, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[5063, 149, 97, 2, 70, "Title", Evaluatable->False], Cell[CellGroupData[{ Cell[5183, 153, 94, 2, 70, "SmallText", Evaluatable->False], Cell[5280, 157, 219, 5, 70, "Input", InitializationCell->True] }, Closed]], Cell[CellGroupData[{ Cell[5531, 164, 89, 2, 70, "Section", Evaluatable->False], Cell[5623, 168, 599, 19, 70, "Text", Evaluatable->False], Cell[CellGroupData[{ Cell[6245, 189, 118, 2, 70, "Input"], Cell[6366, 193, 147, 7, 70, "Output", Evaluatable->False], Cell[6516, 202, 104, 6, 70, "Output", Evaluatable->False] }, Open ]], Cell[6632, 210, 287, 6, 70, "Text", Evaluatable->False], Cell[CellGroupData[{ Cell[6942, 218, 107, 2, 70, "Input"], Cell[7052, 222, 139, 7, 70, "Output", Evaluatable->False], Cell[7194, 231, 108, 6, 70, "Output", Evaluatable->False] }, Open ]], Cell[7314, 239, 247, 5, 70, "Text", Evaluatable->False], Cell[7564, 246, 1687, 51, 70, "Text", Evaluatable->False], Cell[CellGroupData[{ Cell[9274, 299, 67, 1, 70, "Input"], Cell[9344, 302, 130, 7, 70, "Output", Evaluatable->False] }, Open ]], Cell[9486, 311, 170, 4, 70, "SmallText", Evaluatable->False], Cell[CellGroupData[{ Cell[9679, 317, 100, 1, 70, "Input"], Cell[9782, 320, 130, 7, 70, "Output", Evaluatable->False], Cell[9915, 329, 129, 7, 70, "Output", Evaluatable->False] }, Open ]], Cell[10056, 338, 486, 16, 70, "SmallText", Evaluatable->False], Cell[CellGroupData[{ Cell[10565, 356, 64, 1, 70, "Input"], Cell[10632, 359, 104, 6, 70, "Output", Evaluatable->False] }, Open ]], Cell[10748, 367, 740, 24, 70, "SmallText", Evaluatable->False], Cell[CellGroupData[{ Cell[11511, 393, 185, 3, 70, "Input"], Cell[11699, 398, 108, 6, 70, "Output", Evaluatable->False], Cell[11810, 406, 106, 6, 70, "Output", Evaluatable->False] }, Open ]], Cell[11928, 414, 415, 13, 70, "SmallText", Evaluatable->False] }, Closed]], Cell[CellGroupData[{ Cell[12375, 429, 93, 2, 70, "Section", Evaluatable->False], Cell[12471, 433, 588, 18, 70, "SmallText", Evaluatable->False], Cell[13062, 453, 98, 1, 70, "Input"], Cell[13163, 456, 401, 13, 70, "SmallText", Evaluatable->False], Cell[13567, 471, 81, 1, 70, "Input"], Cell[13651, 474, 995, 31, 70, "SmallText", Evaluatable->False], Cell[14649, 507, 71, 1, 70, "Input"], Cell[14723, 510, 361, 13, 70, "SmallText", Evaluatable->False], Cell[15087, 525, 80, 1, 70, "Input"], Cell[15170, 528, 587, 17, 70, "SmallText", Evaluatable->False] }, Open ]], Cell[CellGroupData[{ Cell[15789, 547, 91, 2, 70, "Section", Evaluatable->False], Cell[15883, 551, 691, 20, 70, "SmallText", Evaluatable->False], Cell[16577, 573, 129, 3, 70, "Input"], Cell[16709, 578, 938, 20, 70, "SmallText", Evaluatable->False], Cell[17650, 600, 75, 1, 70, "Input"], Cell[17728, 603, 102, 2, 70, "SmallText", Evaluatable->False], Cell[17833, 607, 75, 1, 70, "Input"], Cell[17911, 610, 420, 13, 70, "SmallText", Evaluatable->False], Cell[18334, 625, 75, 1, 70, "Input"], Cell[18412, 628, 1249, 37, 70, "SmallText", Evaluatable->False], Cell[19664, 667, 102, 1, 70, "Input"], Cell[19769, 670, 180, 4, 70, "SmallText", Evaluatable->False] }, Open ]], Cell[CellGroupData[{ Cell[19981, 676, 100, 2, 70, "Section", Evaluatable->False], Cell[20084, 680, 234, 5, 70, "SmallText", Evaluatable->False], Cell[20321, 687, 131, 3, 70, "Input"], Cell[20455, 692, 125, 2, 70, "SmallText", Evaluatable->False], Cell[20583, 696, 110, 2, 70, "Input"], Cell[20696, 700, 168, 4, 70, "SmallText", Evaluatable->False], Cell[20867, 706, 143, 3, 70, "Input"] }, Open ]] }, Open ]] } ] *) (*********************************************************************** End of Mathematica Notebook file. ***********************************************************************)