Cumulative Frequency Polygon and Histogram Analysis
2015-12-07 10:56
This GeoGebra applet demonstrates how to construct histograms and cumulative frequency curves (polygons) to read and analyze data quartiles (Q1, Q2, Q3). Through dynamic interaction, users can visually understand the concepts of frequency distribution and cumulative frequency, making it an excellent tool for teaching and learning basic statistics.
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<condition showObject="showCF ∧ pointer ≥ 1"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="true" sizeM="1.4" size="8" style="0"/>
<decimals val="1"/>
<startPoint exp="pointOnXaxis"/>
<labelOffset x="3" y="-3"/>
</element>
<expression label="文字5" exp=""" + (x(pointOnXaxis2)) + """ />
<element type="text" label="文字5">
<show object="true" label="false" ev="4"/>
<condition showObject="showCF ∧ pointer ≥ 3"/>
<objColor r="255" g="102" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="true" sizeM="1.4" size="8" style="0"/>
<decimals val="1"/>
<startPoint exp="pointOnXaxis2"/>
<labelOffset x="4" y="-3"/>
</element>
<expression label="文字1" exp=""" + (y(pointOnYaxis2)) + """ />
<element type="text" label="文字1">
<show object="true" label="false" ev="4"/>
<condition showObject="showCF ∧ pointer ≥ 3"/>
<objColor r="255" g="102" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="true" sizeM="1.4" size="8" style="0"/>
<decimals val="0"/>
<startPoint exp="pointOnYaxis2"/>
<labelOffset x="2" y="-4"/>
</element>
<expression label="文字3" exp=""" + (y(pointOnYaxis)) + """ />
<element type="text" label="文字3">
<show object="true" label="false" ev="4"/>
<condition showObject="showCF ∧ pointer ≥ 1"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="true" sizeM="1.4" size="8" style="0"/>
<decimals val="0"/>
<startPoint exp="pointOnYaxis"/>
<labelOffset x="3" y="-3"/>
</element>
<expression label="文字4" exp=""" + (y(pointOnYaxis3)) + """ />
<element type="text" label="文字4">
<show object="true" label="false" ev="4"/>
<condition showObject="showCF ∧ pointer ≥ 2"/>
<objColor r="51" g="51" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="true" sizeM="1.4" size="8" style="0"/>
<decimals val="0"/>
<startPoint exp="pointOnYaxis3"/>
<labelOffset x="3" y="-3"/>
</element>
<expression label="文字CF" exp=""" + (LaTeX[TableText[{c1, c2}, "vc"]]) + """ />
<element type="text" label="文字CF">
<show object="true" label="false" ev="8"/>
<condition showObject="showCF"/>
<objColor r="0" g="155" b="0" alpha="0"/>
<bgColor r="255" g="250" b="205" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="1" size="0" style="0"/>
<absoluteScreenLocation x="588" y="236"/>
</element>
<expression label="文字H" exp=""" + (LaTeX[TableText[{c3, c4, c5}, "vc"]]) + """ />
<element type="text" label="文字H">
<show object="true" label="false" ev="8"/>
<condition showObject="showH"/>
<objColor r="153" g="0" b="153" alpha="0"/>
<bgColor r="255" g="250" b="205" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="1" size="0" style="0"/>
<absoluteScreenLocation x="584" y="46"/>
</element>
<command name="Textfield">
<input a0="a"/>
<output a0="InputBox1"/>
</command>
<element type="textfield" label="InputBox1">
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="14" y="52"/>
<labelMode val="0"/>
<fixed val="true"/>
<isShape val="false"/>
<auxiliary val="true"/>
<linkedGeo exp="a"/>
<length val="4"/>
<caption val="由："/>
</element>
<command name="Textfield">
<input a0="b"/>
<output a0="InputBox2"/>
</command>
<element type="textfield" label="InputBox2">
<show object="true" label="true" ev="3"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="133" y="51"/>
<labelMode val="0"/>
<fixed val="true"/>
<isShape val="false"/>
<auxiliary val="true"/>
<linkedGeo exp="b"/>
<length val="4"/>
<caption val="至："/>
</element>
<expression label="文字7" exp=""" + (LaTeX[If[showH, "頻數", ""]]) + "\\" + (LaTeX[If[showCF, "\textcolor{#009B00}{累積頻數}", ""]]) + """ />
<element type="text" label="文字7">
<show object="true" label="false" ev="8"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1" size="0" style="0"/>
<absoluteScreenLocation x="45" y="19"/>
</element>
<command name="Sequence">
<input a0="a - (b - a) / ((2 * intNum)) + (i * (b - a) / intNum)" a1="i" a2="0" a3="intNum + 1"/>
<output a0="classMidPoint"/>
</command>
<element type="list" label="classMidPoint">
<objColor r="0" g="100" b="0" alpha="0.10000000149011612"/>
<isShape val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<command name="Join">
<input a0="{{0}, freq, {0}}"/>
<output a0="freq0"/>
</command>
<element type="list" label="freq0">
<objColor r="0" g="100" b="0" alpha="0.10000000149011612"/>
<isShape val="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<pointSize val="5"/>
<pointStyle val="-1"/>
</element>
<command name="PolyLine">
<input a0="Zip[(j, k), j, classMidPoint, k, freq0]"/>
<output a0="f"/>
</command>
<element type="polyline" label="f">
<lineStyle thickness="4" type="0" typeHidden="1" opacity="178"/>
<show object="false" label="false" ev="8"/>
<condition showObject="showFP"/>
<objColor r="127" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<selectionAllowed val="false"/>
</element>
<element type="boolean" label="showFP">
<value val="false"/>
<show object="true" label="true" ev="3"/>
<objColor r="127" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelOffset x="535" y="6"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<caption val="頻數多邊形"/>
</element>
<expression label ="Curve" exp="Curve(x) = NaN" type="function"/>
<element type="function" label="Curve">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<isShape val="false"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
</element>
</construction>
</geogebra>