四分位数与箱线图（单组数据）
2015-11-03 00:49
本范例演示如何对一组数据进行描述性统计分析，包括计算最小值、第一四分位数(Q1)、中位数(Q2)、第三四分位数(Q3)和最大值，并绘制箱线图(Box Plot)。通过GeoGebra的BoxPlot、Q1、Median、Q3、Sort、Frequency等命令，动态展示数据的五数概括法。用户可通过交互按钮与列表操作，直观理解数据分布特征、集中趋势与离散程度，适用于概率统计基础教学。
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.286.0" id="b0d9539a-eb18-4b12-901e-a748f33cadf1" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="960" height="660" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0.41515151515151516" orientation="0" />
</panes>
<views>
<view id="4097" visible="false" inframe="true" stylebar="true" location="1,1,1,1" size="400" window="83,103,1114,613" />
<view id="4" toolbar="0 || 2020 , 2021 , 2022 , 66 || 2001 , 2003 , 2002 , 2004 , 2005 || 2040 , 2041 , 2042 , 2044 , 2043" visible="false" inframe="false" stylebar="true" location="1,1" size="300" window="100,100,600,400" />
<view id="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 || 1008 1009 || 66 68 || 6" visible="false" inframe="false" stylebar="false" location="1,3" size="300" window="100,100,600,400" />
<view id="1" visible="true" inframe="false" stylebar="false" location="0" size="274" window="100,100,600,400" />
<view id="2" visible="false" inframe="false" stylebar="true" location="1" size="177" window="100,100,250,400" />
<view id="16" visible="true" inframe="false" stylebar="false" location="2" size="376" window="262,79,500,500" />
<view id="32" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="64" toolbar="0" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="128" visible="false" inframe="true" stylebar="false" location="1" size="480" window="50,50,500,500" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="true" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="43" visible="false" inframe="false" stylebar="false" location="1" size="450" window="50,50,500,500" />
<view id="512" toolbar="0 | 1 501 5 19 , 67 | 2 15 45 18 , 7 37 | 514 3 9 , 13 44 , 47 | 16 | 551 550 11 , 22 , 23 , 55 56 57 , 12 | 69 | 510 511 , 512 513 | 533 531 , 534 532 , 522 523 , 537 536 , 535 | 521 520 | 36 , 38 49 560 | 571 30 29 570 31 33 | 17 | 540 40 41 42 , 27 28 35 , 6 , 502" visible="false" inframe="false" stylebar="true" location="1" size="1107" window="100,100,600,400" />
</views>
<toolbar show="false" items="0 39 | 1 501 67 , 5 19 , 72 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24 20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49 50 , 71 | 30 29 54 32 31 33 | 17 26 62 73 , 14 68 | 25 52 60 61 | 40 41 42 , 27 28 35 , 6" position="1" help="false" />
<input show="false" cmd="true" top="true" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="3"/>
<font size="24"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="958" height="274"/>
<coordSystem xZero="30.591557401105224" yZero="179.5412193334641" scale="44.16635632448657" yscale="53.10716386793129"/>
<evSettings axes="true" grid="false" gridIsBold="false" pointCapturing="2" rightAngleStyle="1" checkboxSize="26" gridType="0"/>
<bgColor r="255" g="255" b="255"/>
<axesColor r="0" g="0" b="0"/>
<gridColor r="192" g="192" b="192"/>
<lineStyle axes="3" grid="10"/>
<axis id="0" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true" tickDistance="1" tickExpression="" positiveAxis="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true" positiveAxis="true"/>
<grid distX="1" distY="0.25" distTheta="0.5235987755982988"/>
</euclidianView>
<euclidianView>
<viewNumber viewNo="2"/>
<size width="958" height="376"/>
<coordSystem xZero="41.963291615579145" yZero="85.2743348938841" scale="49.480382790316874" yscale="49.48038279031696"/>
<evSettings axes="false" grid="false" gridIsBold="false" pointCapturing="1" rightAngleStyle="1" checkboxSize="26" gridType="0"/>
<bgColor r="255" g="255" b="255"/>
<axesColor r="0" g="0" b="0"/>
<gridColor r="192" g="192" b="192"/>
<lineStyle axes="1" grid="0"/>
<axis id="0" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<axis id="1" show="false" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
<grid distX="1" distY="0.25" distTheta="0.5235987755982988"/>
</euclidianView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="2" spreadsheet="2"/>
<coordStyle val="0"/>
<angleFromInvTrig val="false"/>
</kernel>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<expression label ="listNx" exp="{5, 6, 7, 8, 9, 10, 11, 12}"/>
<element type="list" label="listNx">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelOffset x="31" y="219"/>
<labelMode val="3"/>
<animation step="1" speed="1" type="0" playing="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<selectedIndex val="7"/>
<comboBox val="true"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
<caption val="Number of data="/>
</element>
<command name="SelectedElement">
<input a0="listNx"/>
<output a0="nX"/>
</command>
<element type="numeric" label="nX">
<value val="12"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<selectionAllowed val="false"/>
</element>
<element type="numeric" label="seperation">
<value val="0.25"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="255" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="-5" max="5" absoluteScreenLocation="true" width="200" x="30" y="90" fixed="false" horizontal="true" showAlgebra="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<command name="Sequence">
<input a0="Segment[(0, i), (20, i)]" a1="i" a2="seperation" a3="(nX * seperation)" a4="seperation"/>
<output a0="listGridX"/>
</command>
<element type="list" label="listGridX">
<show object="true" label="true" ev="4"/>
<objColor r="192" g="192" b="192" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<command name="Point">
<input a0="listGridX"/>
<output a0="L"/>
</command>
<element type="point" label="L">
<show object="true" label="false" ev="4"/>
<condition showObject="nX ≥ 12"/>
<objColor r="128" g="128" b="128" alpha="0"/>
<layer val="9"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="9" y="0.25" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="listGridX"/>
<output a0="K"/>
</command>
<element type="point" label="K">
<show object="true" label="false" ev="4"/>
<condition showObject="nX ≥ 11"/>
<objColor r="128" g="128" b="128" alpha="0"/>
<layer val="9"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="3" y="0.25" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="listGridX"/>
<output a0="J"/>
</command>
<element type="point" label="J">
<show object="true" label="false" ev="4"/>
<condition showObject="nX ≥ 10"/>
<objColor r="128" g="128" b="128" alpha="0"/>
<layer val="9"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="2.9999999999999982" y="0.5" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="listGridX"/>
<output a0="I"/>
</command>
<element type="point" label="I">
<show object="true" label="false" ev="4"/>
<condition showObject="nX ≥ 9"/>
<objColor r="128" g="128" b="128" alpha="0"/>
<layer val="9"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="0" y="0.5" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="listGridX"/>
<output a0="H"/>
</command>
<element type="point" label="H">
<show object="true" label="false" ev="4"/>
<condition showObject="nX ≥ 8"/>
<objColor r="128" g="128" b="128" alpha="0"/>
<layer val="9"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="2" y="0.25" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="listGridX"/>
<output a0="G"/>
</command>
<element type="point" label="G">
<show object="true" label="false" ev="4"/>
<condition showObject="nX ≥ 7"/>
<objColor r="128" g="128" b="128" alpha="0"/>
<layer val="9"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="19" y="0.5" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="listGridX"/>
<output a0="F"/>
</command>
<element type="point" label="F">
<show object="false" label="false" ev="4"/>
<condition showObject="nX ≥ 6"/>
<objColor r="128" g="128" b="128" alpha="0"/>
<layer val="9"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="17" y="0.25" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="listGridX"/>
<output a0="E"/>
</command>
<element type="point" label="E">
<show object="true" label="false" ev="4"/>
<condition showObject="nX ≥ 5"/>
<objColor r="128" g="128" b="128" alpha="0"/>
<layer val="9"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="4" y="0.25" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="listGridX"/>
<output a0="D"/>
</command>
<element type="point" label="D">
<show object="true" label="false" ev="4"/>
<condition showObject="nX ≥ 4"/>
<objColor r="128" g="128" b="128" alpha="0"/>
<layer val="9"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="15" y="0.25" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="listGridX"/>
<output a0="C"/>
</command>
<element type="point" label="C">
<show object="true" label="false" ev="4"/>
<objColor r="128" g="128" b="128" alpha="0"/>
<layer val="9"/>
<labelOffset x="-8" y="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="19" y="0.25" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="listGridX"/>
<output a0="B"/>
</command>
<element type="point" label="B">
<show object="true" label="false" ev="4"/>
<objColor r="128" g="128" b="128" alpha="0"/>
<layer val="9"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="9" y="0.5" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="listGridX"/>
<output a0="A"/>
</command>
<element type="point" label="A">
<show object="true" label="false" ev="4"/>
<objColor r="128" g="128" b="128" alpha="0"/>
<layer val="9"/>
<labelOffset x="21" y="47"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="8" y="0.25" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Take">
<input a0="Zip[x(k), k, {A, B, C, D, E, F, G, H, I, J, K, L}]" a1="1" a2="nX"/>
<output a0="listDataX"/>
</command>
<element type="list" label="listDataX">
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<command name="Mean">
<input a0="listDataX"/>
<output a0="meanX"/>
</command>
<element type="numeric" label="meanX">
<value val="9"/>
<objColor r="0" g="0" b="255" alpha="0.1"/>
<selectionAllowed val="false"/>
</element>
<element type="boolean" label="box1">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="37" y="142"/>
<labelMode val="3"/>
<checkbox fixed="true"/>
<caption val="Lower Quartile"/>
</element>
<element type="boolean" label="box2">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="334" y="142"/>
<labelMode val="3"/>
<checkbox fixed="true"/>
<caption val="Median"/>
</element>
<element type="button" label="button1">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="255" b="0" alpha="255"/>
<layer val="0"/>
<labelOffset x="331" y="219"/>
<labelMode val="3"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<ggbscript val="UpdateConstruction[] SetValue[A,listPosition(1)] SetValue[B,listPosition(2)] SetValue[C,listPosition(3)] SetValue[D,listPosition(4)] SetValue[E,listPosition(5)] SetValue[F,listPosition(6)] SetValue[G,listPosition(7)] SetValue[H,listPosition(8)] SetValue[I,listPosition(9)] SetValue[J,listPosition(10)] SetValue[K,listPosition(11)] SetValue[L,listPosition(12)] SetValue[box1,false] SetValue[box2,false] SetValue[box3,false] SetValue[box4,false] SetValue[box5,false] SetValue[box6,false] SetValue[Q_1,(0,0)] SetValue[Q_2,(1,0)] SetValue[Q_3,(2,0)]"/>
<font serif="false" sizeM="2" size="24" style="0"/>
<caption val="Random data"/>
</element>
<command name="Take">
<input a0="Zip[k, k, {A, B, C, D, E, F, G, H, I, J, K, L}]" a1="1" a2="nX"/>
<output a0="listDataPointX"/>
</command>
<element type="list" label="listDataPointX">
<show object="false" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<element type="boolean" label="box3">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="631" y="142"/>
<labelMode val="3"/>
<checkbox fixed="true"/>
<caption val="Upper Quartile"/>
</element>
<element type="button" label="button2">
<show object="true" label="true"/>
<condition showObject="¬reachMax"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="0" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelOffset x="546" y="219"/>
<labelMode val="3"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[A,A+(1,0)] SetValue[B,B+(1,0)] SetValue[C,C+(1,0)] SetValue[D,D+(1,0)] SetValue[E,E+(1,0)] SetValue[F,F+(1,0)] SetValue[G,G+(1,0)] SetValue[H,H+(1,0)] SetValue[I,I+(1,0)] SetValue[J,J+(1,0)] SetValue[K,K+(1,0)] SetValue[L,L+(1,0)]"/>
<font serif="false" sizeM="1.4" size="10" style="0"/>
<caption val="Add 1 to all data"/>
</element>
<element type="button" label="button3">
<show object="true" label="true"/>
<condition showObject="¬reachMin"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="0" g="255" b="255" alpha="255"/>
<layer val="0"/>
<labelOffset x="719" y="219"/>
<labelMode val="3"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[A,A-(1,0)] SetValue[B,B-(1,0)] SetValue[C,C-(1,0)] SetValue[D,D-(1,0)] SetValue[E,E-(1,0)] SetValue[F,F-(1,0)] SetValue[G,G-(1,0)] SetValue[H,H-(1,0)] SetValue[I,I-(1,0)] SetValue[J,J-(1,0)] SetValue[K,K-(1,0)] SetValue[L,L-(1,0)]"/>
<font serif="false" sizeM="1.4" size="10" style="0"/>
<caption val="Subtract 1 from all data"/>
</element>
<element type="numeric" label="rem">
<value val="1"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="0"/>
<labelMode val="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<expression label="reachMin" exp="Min[listDataX] ≤ 0" />
<element type="boolean" label="reachMin">
<value val="true"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<expression label="reachMax" exp="Max[listDataX] ≥ 20" />
<element type="boolean" label="reachMax">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<command name="If">
<input a0="nX ≥ 11" a1="0.7" a2="If[nX ≥ 9, 0.85, 1]"/>
<output a0="scale"/>
</command>
<element type="numeric" label="scale">
<value val="0.7"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<selectionAllowed val="false"/>
</element>
<command name="Q1">
<input a0="listDataX"/>
<output a0="q1"/>
</command>
<element type="numeric" label="q1">
<value val="2.999999999999999"/>
<objColor r="255" g="127" b="0" alpha="0.1"/>
<selectionAllowed val="false"/>
</element>
<command name="Median">
<input a0="listDataX"/>
<output a0="q2"/>
</command>
<element type="numeric" label="q2">
<value val="8.5"/>
<objColor r="255" g="127" b="0" alpha="0.1"/>
<selectionAllowed val="false"/>
</element>
<command name="Q3">
<input a0="listDataX"/>
<output a0="q3"/>
</command>
<element type="numeric" label="q3">
<value val="16"/>
<objColor r="255" g="127" b="0" alpha="0.1"/>
<selectionAllowed val="false"/>
</element>
<command name="Min">
<input a0="listDataX"/>
<output a0="minval"/>
</command>
<element type="numeric" label="minval">
<value val="0"/>
<objColor r="255" g="127" b="0" alpha="0.1"/>
<selectionAllowed val="false"/>
</element>
<command name="Max">
<input a0="listDataX"/>
<output a0="maxval"/>
</command>
<element type="numeric" label="maxval">
<value val="19"/>
<objColor r="255" g="127" b="0" alpha="0.1"/>
<selectionAllowed val="false"/>
</element>
<expression label="text3" exp=""Q_{1}=" + (LaTeX[Text[q1]]) + """ />
<element type="text" label="text3">
<show object="true" label="false" ev="11"/>
<condition showObject="box1"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<absoluteScreenLocation x="70" y="187"/>
</element>
<expression label="text4" exp=""Q_{2}=" + (LaTeX[Text[q2]]) + """ />
<element type="text" label="text4">
<show object="true" label="false" ev="11"/>
<condition showObject="box2"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<absoluteScreenLocation x="367" y="187"/>
</element>
<expression label="text5" exp=""Q_{3}=" + (LaTeX[Text[q3]]) + """ />
<element type="text" label="text5">
<show object="true" label="false" ev="11"/>
<condition showObject="box3"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<absoluteScreenLocation x="663" y="187"/>
</element>
<element type="boolean" label="box4">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="9"/>
<labelOffset x="37" y="241"/>
<labelMode val="3"/>
<checkbox fixed="true"/>
<caption val="Interquartile Range"/>
</element>
<element type="boolean" label="box5">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="9"/>
<labelOffset x="334" y="241"/>
<labelMode val="3"/>
<checkbox fixed="true"/>
<caption val="Range"/>
</element>
<element type="boolean" label="box6">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="9"/>
<labelOffset x="631" y="241"/>
<labelMode val="3"/>
<checkbox fixed="true"/>
<caption val="Box Plot"/>
</element>
<expression label="text2" exp=""=" + (LaTeX[q3]) + "-" + (LaTeX[q1]) + "\\=" + (LaTeX[q3 - q1]) + """ />
<element type="text" label="text2">
<show object="true" label="false" ev="11"/>
<condition showObject="box4"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="9"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<absoluteScreenLocation x="69" y="287"/>
</element>
<expression label="text6" exp=""=" + (LaTeX[maxval]) + "-" + (LaTeX[minval]) + "\\ =" + (LaTeX[maxval - minval]) + """ />
<element type="text" label="text6">
<show object="true" label="false" ev="11"/>
<condition showObject="box5"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="9"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<absoluteScreenLocation x="368" y="288"/>
</element>
<command name="Ray">
<input a0="(0, 0)" a1="(1, 0)"/>
<output a0="b"/>
</command>
<element type="ray" label="b">
<show object="false" label="false" ev="7"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="9"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="0" y="1" z="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Point">
<input a0="b"/>
<output a0="Q_2"/>
</command>
<element type="point" label="Q_2">
<show object="true" label="true" ev="7"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="9"/>
<labelOffset x="-13" y="38"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="1" y="0" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="b"/>
<output a0="Q_3"/>
</command>
<element type="point" label="Q_3">
<show object="true" label="true" ev="7"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="9"/>
<labelOffset x="-12" y="39"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="2" y="0" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Point">
<input a0="b"/>
<output a0="Q_1"/>
</command>
<element type="point" label="Q_1">
<show object="true" label="true" ev="7"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="9"/>
<labelOffset x="-13" y="38"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<coords x="0" y="0" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<command name="Vector">
<input a0="Q_1" a1="Q_1 + (0, 0.8)"/>
<output a0="u"/>
</command>
<element type="vector" label="u">
<show object="true" label="false" ev="7"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="9"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="0" y="0.8" z="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<coordStyle style="cartesian"/>
<startPoint exp="Q_1"/>
</element>
<command name="Vector">
<input a0="Q_2" a1="Q_2 + (0, 0.8)"/>
<output a0="v"/>
</command>
<element type="vector" label="v">
<show object="true" label="false" ev="7"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="9"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="0" y="0.8" z="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<coordStyle style="cartesian"/>
<startPoint exp="Q_2"/>
</element>
<command name="Vector">
<input a0="Q_3" a1="Q_3 + (0, 0.8)"/>
<output a0="w"/>
</command>
<element type="vector" label="w">
<show object="true" label="false" ev="7"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="9"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="0" y="0.8" z="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<coordStyle style="cartesian"/>
<startPoint exp="Q_3"/>
</element>
<command name="Sequence">
<input a0="Random[0, 20]" a1="i" a2="1" a3="nX"/>
<output a0="listRand"/>
</command>
<element type="list" label="listRand">
<objColor r="0" g="100" b="0" alpha="0.1"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
<symbolic val="true" />
</element>
<command name="Sort">
<input a0="listRand"/>
<output a0="listRandSort"/>
</command>
<element type="list" label="listRandSort">
<objColor r="0" g="100" b="0" alpha="0.1"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<command name="Frequency">
<input a0="listRand"/>
<output a0="listFreq"/>
</command>
<element type="list" label="listFreq">
<objColor r="0" g="100" b="0" alpha="0.1"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<command name="Flatten">
<input a0="Zip[Sequence[(seperation * i), i, 1, k], k, listFreq]"/>
<output a0="listHeight"/>
</command>
<element type="list" label="listHeight">
<objColor r="0" g="100" b="0" alpha="0.1"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<command name="Shuffle">
<input a0="Zip[(h, k), h, listRandSort, k, listHeight]"/>
<output a0="listPosition"/>
</command>
<element type="list" label="listPosition">
<show object="false" label="false"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<bgColor r="255" g="255" b="255" alpha="255"/>
<layer val="8"/>
<labelMode val="0"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="3"/>
<pointStyle val="-1"/>
</element>
<command name="BoxPlot">
<input a0="2.4" a1="0.6" a2="listDataX"/>
<output a0="boxplot"/>
</command>
<element type="numeric" label="boxplot">
<value val="8.5"/>
<show object="true" label="false"/>
<condition showObject="box6"/>
<objColor r="0" g="0" b="255" alpha="0.25"/>
<layer val="0"/>
<labelMode val="1"/>
<lineStyle thickness="4" type="0" typeHidden="1"/>
<selectionAllowed val="false"/>
</element>
<command name="Segment">
<input a0="(maxval, 0)" a1="(maxval, 1.25)"/>
<output a0="maxLine"/>
</command>
<element type="segment" label="maxLine">
<show object="true" label="false" ev="8"/>
<condition showObject="box5"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="-1.25" y="0" z="23.75"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="(q3, 0)" a1="(q3, 1.25)"/>
<output a0="q3Line"/>
</command>
<element type="segment" label="q3Line">
<show object="true" label="false" ev="4"/>
<condition showObject="box3"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="-1.25" y="0" z="20"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="(q2, 0)" a1="(q2, 1.25)"/>
<output a0="q2Line"/>
</command>
<element type="segment" label="q2Line">
<show object="true" label="false" ev="4"/>
<condition showObject="box2"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="-1.25" y="0" z="10.625"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="(q1, 0)" a1="(q1, 1.25)"/>
<output a0="q1Line"/>
</command>
<element type="segment" label="q1Line">
<show object="true" label="false" ev="8"/>
<condition showObject="box1"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="-1.25" y="0" z="3.749999999999999"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="(minval, 0)" a1="(minval, 1.25)"/>
<output a0="minLine"/>
</command>
<element type="segment" label="minLine">
<show object="true" label="false" ev="8"/>
<condition showObject="box5"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="1"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<coords x="-1.25" y="0" z="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<element type="numeric" label="lang">
<value val="2"/>
<symbolic val="true" />
<show object="false" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0.1"/>
<layer val="8"/>
<labelMode val="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="button" label="button0">
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="8"/>
<labelOffset x="874" y="85"/>
<labelMode val="3"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue[lang,If[lang==1,2,1]] RunClickScript[buttonLang] "/>
<font serif="false" sizeM="1.4" size="10" style="0"/>
<caption val="中文"/>
</element>
<element type="button" label="buttonLang">
<show object="false" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="8"/>
<labelOffset x="858" y="83"/>
<labelMode val="0"/>
<animation step="1" speed="1" type="0" playing="false"/>
<auxiliary val="true"/>
<ggbscript val="SetCaption[button0,If[lang==1,"ENG","中文"]] SetCaption[listNx,If[lang==1,"數據數目=","Number of data="]] SetCaption[button2,If[lang==1,"所有數據加1","Add 1 to all data"]] SetCaption[button3,If[lang==1,"所有數據減1","Subtract 1 from all data"]] SetCaption[button1,If[lang==1,"隨機數據","Random data"]] SetCaption[box1,If[lang==1,"下四分位數","Lower Quartile"]] SetCaption[box2,If[lang==1,"中位數","Median"]] SetCaption[box3,If[lang==1,"上四分位數","Upper Quartile"]] SetCaption[box4,If[lang==1,"四分位數間距","Interquartile Range"]] SetCaption[box5,If[lang==1,"分佈域","Range"]] SetCaption[box6,If[lang==1,"框線圖","Box Plot"]]"/>
<font serif="false" sizeM="1.4" size="10" style="0"/>
</element>
<expression label="text1" exp=""" + (LaTeX[If[lang ≟ 1, "\text{數據（已排序）： }", "\text{Data (sorted): }"]]) + "" + (LaTeX[TableText[{Sort[listDataX]}, "c"]]) + """ />
<element type="text" label="text1">
<show object="true" label="false" ev="11"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<bgColor r="255" g="250" b="205" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="1"/>
<absoluteScreenLocation x="30" y="9"/>
</element>
</construction>
</geogebra>