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text-align="inherit" list-style-type="inherit" tabs="inherit"><f family="Arial" charset="0"><u><inlineAttr line-through="false"><c val="#808000"><link href="./desc_stats.xmcd" title="Links to Section Contents" popup="false"><sp count="4" />DESCRIPTIVE STATISTICS</link></c></inlineAttr></u></f></p></text></region><region region-id="114" left="36" top="72.75" width="45" height="13.5" align-x="36" align-y="84" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="Sous-titre" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Location</p></text><indexes><phrase>location</phrase><phrase>descriptive statistics, location</phrase><phrase>statistics, descriptive, location</phrase><phrase>mean</phrase><phrase>arithmetic mean</phrase><phrase>average</phrase><phrase>median</phrase><phrase>mode</phrase><phrase>percentile</phrase><phrase>functions, mean</phrase><phrase>functions, median</phrase><phrase>functions, mode</phrase><phrase>functions, percentile</phrase><phrase>measures of location</phrase><phrase>multimodal</phrase><phrase>quartiles</phrase></indexes></region><region region-id="107" left="66" top="97.5" width="72.75" height="12.75" align-x="66" align-y="108" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="functions" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">mean(A,B,C,...)</p></text></region><region region-id="685" left="156" top="97.5" width="81" height="12.75" align-x="156" align-y="108" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="functions" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">median(A,B,C,...)</p></text></region><region region-id="109" left="66" top="115.5" width="72" height="12.75" align-x="66" align-y="126" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="functions" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">mode(A,B,C,...)</p></text></region><region region-id="686" left="156" top="115.5" width="66.75" height="12.75" align-x="156" align-y="126" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="functions" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">percentile(v,p)</p></text></region><region region-id="437" left="36" top="146.25" width="293.25" height="72" align-x="36" align-y="156" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">These functions take single or multiple scalars or arrays, and return the mean, median, and mode, respectively, giving measures of the location of a data point relative to the rest of the distribution. The best choice of location estimator depends on the general <f family="Verdana" charset="0"><b><u><inlineAttr line-through="false"><c val="#000"><link href="./dispersion.xmcd" title="Links to section" popup="false">dispersion</link></c></inlineAttr></u></b></f> or distribution of your data.</p></text></region><region region-id="687" left="36" top="229.5" width="28.5" height="12.75" align-x="47.25" align-y="240" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="subsubtitle" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Mean </p></text></region><region region-id="390" left="36" top="248.25" width="201" height="12" align-x="36" align-y="258" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">For a set of numeric data, for example:</p></text></region><region region-id="392" left="66" top="276" width="51.75" height="78.75" align-x="87" align-y="318" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><math optimize="false" disable-calc="false"><ml:define><ml:id xml:space="preserve">mfg</ml:id><ml:matrix rows="5" cols="1"><ml:real>79</ml:real><ml:real>85</ml:real><ml:real>46</ml:real><ml:real>86</ml:real><ml:real>81</ml:real></ml:matrix></ml:define></math><rendering item-idref="4" /></region><region region-id="435" left="180" top="309" width="69" height="12.75" align-x="193.5" align-y="318" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><math optimize="false" disable-calc="false"><ml:define warning="WarnRedefinedBIUnit"><ml:id xml:space="preserve">N</ml:id><ml:apply><ml:id xml:space="preserve">length</ml:id><ml:id xml:space="preserve">mfg</ml:id></ml:apply></ml:define></math><rendering item-idref="5" /></region><region region-id="397" left="36" top="362.25" width="289.5" height="24" align-x="36" align-y="372" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">the arithmetic mean or average of the N values in x is given by </p></text></region><region region-id="403" left="66" top="397.5" width="99.75" height="43.5" align-x="137.25" align-y="420" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><math optimize="false" disable-calc="false"><ml:eval><ml:apply><ml:mult style="default" /><ml:apply><ml:div /><ml:real>1</ml:real><ml:id xml:space="preserve">N</ml:id></ml:apply><ml:parens><ml:apply><ml:summation /><ml:lambda><ml:boundVars><ml:id xml:space="preserve">i</ml:id></ml:boundVars><ml:apply><ml:indexer /><ml:id xml:space="preserve">mfg</ml:id><ml:id xml:space="preserve">i</ml:id></ml:apply></ml:lambda><ml:bounds><ml:real>0</ml:real><ml:apply><ml:minus /><ml:id xml:space="preserve">N</ml:id><ml:real>1</ml:real></ml:apply></ml:bounds></ml:apply></ml:parens></ml:apply><result xmlns="http://schemas.mathsoft.com/math20"><ml:real>75.4</ml:real></result></ml:eval></math><rendering item-idref="6" /></region><region region-id="436" left="180" top="411" width="77.25" height="12.75" align-x="228.75" align-y="420" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><math optimize="false" disable-calc="false"><ml:eval><ml:apply><ml:id xml:space="preserve">mean</ml:id><ml:id xml:space="preserve">mfg</ml:id></ml:apply><result xmlns="http://schemas.mathsoft.com/math20"><ml:real>75.4</ml:real></result></ml:eval></math><rendering item-idref="7" /></region><region region-id="491" left="36" top="458.25" width="282" height="24" align-x="36" align-y="468" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"><f family="Verdana" charset="0"><b><inlineAttr line-through="false"><c val="#000">mean</c></inlineAttr></b></f> is sensitive to change in the value of one or more data points:</p></text></region><region region-id="492" left="66" top="501" width="66.75" height="18" align-x="91.5" align-y="510" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><math optimize="false" disable-calc="false"><ml:define warning="WarnRedefinedUDScalar"><ml:apply><ml:indexer /><ml:id xml:space="preserve">mfg</ml:id><ml:real>2</ml:real></ml:apply><ml:apply><ml:mult style="default" /><ml:real>1.2</ml:real><ml:apply><ml:indexer /><ml:id xml:space="preserve">mfg</ml:id><ml:real>2</ml:real></ml:apply></ml:apply></ml:define></math><rendering item-idref="8" /></region><region region-id="494" left="180" top="501" width="81.75" height="12.75" align-x="228.75" align-y="510" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><math optimize="false" disable-calc="false"><ml:eval><ml:apply><ml:id xml:space="preserve">mean</ml:id><ml:id xml:space="preserve">mfg</ml:id></ml:apply><result xmlns="http://schemas.mathsoft.com/math20"><ml:real>77.240000000000009</ml:real></result></ml:eval></math><rendering item-idref="9" /></region><region region-id="571" left="36" top="530.25" width="275.25" height="48" align-x="36" align-y="540" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">If your data set has significant <b><u><link href="./outlier.xmcd" title="Links to section" popup="false">outliers</link></u></b>, you may find the mean a poor description of the central location. You can trim the outliers, and find the "trimmed mean" for a better estimate.</p></text></region><region region-id="619" left="0" top="588" width="6000" height="6" align-x="0" align-y="588" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><pageBreak /></region><region region-id="259" left="36" top="601.5" width="33.75" height="12.75" align-x="36" align-y="612" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="median"><text use-page-width="false" push-down="false" lock-width="true"><p style="subsubtitle" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Median</p></text><indexes><phrase>median</phrase></indexes></region><region region-id="300" left="36" top="626.25" width="285.75" height="72" align-x="36" align-y="636" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">The median, or "middle value," of a set of data is another metric for central location. It is less sensitive to outliers or small changes in data. A median is the value falling in the middle when data are <b><u><link href="./sorting.xmcd" title="Links to section" popup="false">sorted</link></u></b> in ascending order. If there are an odd number of data, there is one data value which is the median. </p></text></region><region region-id="515" left="66" top="747" width="78" height="12.75" align-x="122.25" align-y="756" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><math optimize="false" disable-calc="false"><ml:eval><ml:apply><ml:id xml:space="preserve">median</ml:id><ml:id xml:space="preserve">mfg</ml:id></ml:apply><result xmlns="http://schemas.mathsoft.com/math20"><ml:real>81</ml:real></result></ml:eval></math><rendering item-idref="10" /></region><region region-id="698" left="180" top="714" width="86.25" height="78.75" align-x="223.5" align-y="756" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><math optimize="false" disable-calc="false"><ml:eval><ml:apply><ml:id xml:space="preserve">sort</ml:id><ml:id xml:space="preserve">mfg</ml:id></ml:apply><result xmlns="http://schemas.mathsoft.com/math20"><ml:matrix rows="5" cols="1"><ml:real>55.199999999999996</ml:real><ml:real>79</ml:real><ml:real>81</ml:real><ml:real>85</ml:real><ml:real>86</ml:real></ml:matrix></result></ml:eval></math><rendering item-idref="11" /></region><region region-id="568" left="36" top="806.25" width="303" height="60" align-x="36" align-y="816" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">The median depends on the relative positions of the data, not on the actual values of every data point, and so is relatively insensitive to small changes in individual data values. Mathcad's <f family="Verdana" charset="0"><b><inlineAttr line-through="false"><c val="#000">median</c></inlineAttr></b></f> function does not accept complex numbers.</p></text></region><region region-id="688" left="36" top="878.25" width="294.75" height="60" align-x="36" align-y="888" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">In the case of an even number of data there is not a unique median. Median values are those that lie between the middle two data values. The convention with data sets containing an even number of data points is to find the average of the two middle data points.</p></text></region><region region-id="589" left="36" top="961.5" width="24.75" height="12.75" align-x="47.25" align-y="972" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="subsubtitle" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Mode</p></text><indexes><phrase>mode</phrase></indexes></region><region region-id="591" left="36" top="980.25" width="307.5" height="24" align-x="43.5" align-y="990" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">The <f family="Verdana" charset="0"><b><inlineAttr line-through="false"><c val="#000">mode</c></inlineAttr></b></f> of a data set is the value that occurs with greatest frequency.</p></text></region><region region-id="593" left="66" top="1017" width="66.75" height="12.75" align-x="115.5" align-y="1026" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><math error="no duplicates" optimize="false" disable-calc="false"><ml:eval><ml:apply><ml:id xml:space="preserve">mode</ml:id><ml:id xml:space="preserve">mfg</ml:id></ml:apply></ml:eval></math><rendering item-idref="12" /></region><region region-id="595" left="36" top="1040.25" width="289.5" height="60" align-x="36" align-y="1050" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">In a data set where there are no repeated values, you see an error message like the one shown above. In the case where more than one data value is repeated with the same frequency, the <b>mode</b> function also gives an error, with the message "multimodal."</p></text><indexes><phrase>multimodal error message</phrase></indexes></region><region region-id="605" left="66" top="1113" width="51" height="12.75" align-x="74.25" align-y="1122" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><math optimize="false" disable-calc="false"><ml:define><ml:id xml:space="preserve">i</ml:id><ml:range><ml:real>0</ml:real><ml:apply><ml:minus /><ml:id xml:space="preserve">N</ml:id><ml:real>1</ml:real></ml:apply></ml:range></ml:define></math><rendering item-idref="13" /></region><region region-id="603" left="66" top="1137" width="52.5" height="18" align-x="93.75" align-y="1146" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><math optimize="false" disable-calc="false"><ml:define><ml:apply><ml:indexer /><ml:id xml:space="preserve">mfg2</ml:id><ml:id xml:space="preserve">i</ml:id></ml:apply><ml:apply><ml:indexer /><ml:id xml:space="preserve">mfg</ml:id><ml:id xml:space="preserve">i</ml:id></ml:apply></ml:define></math><rendering item-idref="14" /></region><region region-id="611" left="144" top="1137" width="66" height="18" align-x="185.25" align-y="1146" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><math optimize="false" disable-calc="false"><ml:define warning="WarnRedefinedUDScalar"><ml:apply><ml:indexer /><ml:id xml:space="preserve">mfg2</ml:id><ml:apply><ml:plus /><ml:id xml:space="preserve">i</ml:id><ml:id xml:space="preserve">N</ml:id></ml:apply></ml:apply><ml:apply><ml:indexer /><ml:id xml:space="preserve">mfg</ml:id><ml:id xml:space="preserve">i</ml:id></ml:apply></ml:define></math><rendering item-idref="15" /></region><region region-id="613" left="66" top="1167" width="71.25" height="12.75" align-x="120" align-y="1176" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><math error="multimodal" optimize="false" disable-calc="false"><ml:eval><ml:apply><ml:id xml:space="preserve">mode</ml:id><ml:id xml:space="preserve">mfg2</ml:id></ml:apply></ml:eval></math><rendering item-idref="16" /></region><region region-id="621" left="0" top="1194" width="6000" height="6" align-x="0" align-y="1194" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><pageBreak /></region><region region-id="623" left="36" top="1201.5" width="117" height="12.75" align-x="54.75" align-y="1212" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="quantiles"><text use-page-width="false" push-down="false" lock-width="true"><p style="subsubtitle" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Percentiles and Quartiles</p></text><indexes><phrase>percentiles</phrase><phrase>quartiles</phrase></indexes></region><region region-id="632" left="36" top="1220.25" width="296.25" height="84" align-x="36" align-y="1230" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Percentiles measure which values of a data set fall below a certain percentage of the total number of points. So, if your data set has 11 points, the 50th percentile is the value of the median, or 6th point, and so on. The <f family="Verdana" charset="0"><b><inlineAttr line-through="false"><c val="#000">percentile</c></inlineAttr></b></f> function takes a vector of data and a percentage between 0 and 1 and returns the value of the percentile.</p></text></region><region region-id="643" left="66" top="1317" width="36.75" height="12.75" align-x="74.25" align-y="1326" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><math optimize="false" disable-calc="false"><ml:define warning="WarnRedefinedUDScalar"><ml:id xml:space="preserve">i</ml:id><ml:range><ml:real>0</ml:real><ml:real>10</ml:real></ml:range></ml:define></math><rendering item-idref="17" /></region><region region-id="642" left="144" top="1317" width="21.75" height="18" align-x="156" align-y="1326" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><math optimize="false" disable-calc="false"><ml:define><ml:apply><ml:indexer /><ml:id xml:space="preserve">x</ml:id><ml:id xml:space="preserve">i</ml:id></ml:apply><ml:id xml:space="preserve">i</ml:id></ml:define></math><rendering item-idref="18" /></region><region region-id="653" left="144" top="1383" width="93" height="12.75" align-x="219.75" align-y="1392" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><math optimize="false" disable-calc="false"><ml:eval><ml:apply><ml:id xml:space="preserve">percentile</ml:id><ml:sequence><ml:id xml:space="preserve">x</ml:id><ml:real>0.50</ml:real></ml:sequence></ml:apply><result xmlns="http://schemas.mathsoft.com/math20"><ml:real>5</ml:real></result></ml:eval></math><rendering item-idref="19" /></region><region region-id="696" left="258" top="1383" width="94.5" height="12.75" align-x="335.25" align-y="1392" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><math optimize="false" disable-calc="false"><ml:eval><ml:apply><ml:id xml:space="preserve">percentile</ml:id><ml:sequence><ml:id xml:space="preserve">x</ml:id><ml:apply><ml:mult style="auto-select" /><ml:real>50</ml:real><ml:id xml:space="preserve">%</ml:id></ml:apply></ml:sequence></ml:apply><result xmlns="http://schemas.mathsoft.com/math20"><ml:real>5</ml:real></result></ml:eval></math><rendering item-idref="20" /></region><region region-id="654" left="144" top="1407" width="62.25" height="12.75" align-x="189" align-y="1416" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><math optimize="false" disable-calc="false"><ml:eval><ml:apply><ml:id xml:space="preserve">median</ml:id><ml:id xml:space="preserve">x</ml:id></ml:apply><result xmlns="http://schemas.mathsoft.com/math20"><ml:real>5</ml:real></result></ml:eval></math><rendering item-idref="21" /></region><region region-id="645" left="66" top="1344" width="66.75" height="181.5" align-x="75" align-y="1434" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><math optimize="false" disable-calc="false"><ml:eval><ml:id xml:space="preserve">x</ml:id><result xmlns="http://schemas.mathsoft.com/math20"><ml:matrix rows="11" cols="1"><ml:real>0</ml:real><ml:real>1</ml:real><ml:real>2</ml:real><ml:real>3</ml:real><ml:real>4</ml:real><ml:real>5</ml:real><ml:real>6</ml:real><ml:real>7</ml:real><ml:real>8</ml:real><ml:real>9</ml:real><ml:real>10</ml:real></ml:matrix></result></ml:eval><resultFormat><table item-idref="22" /></resultFormat></math><rendering item-idref="23" /></region><region region-id="693" left="144" top="1437" width="93" height="12.75" align-x="219.75" align-y="1446" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><math optimize="false" disable-calc="false"><ml:eval><ml:apply><ml:id xml:space="preserve">percentile</ml:id><ml:sequence><ml:id xml:space="preserve">x</ml:id><ml:real>0.25</ml:real></ml:sequence></ml:apply><result xmlns="http://schemas.mathsoft.com/math20"><ml:real>2</ml:real></result></ml:eval></math><rendering item-idref="24" /></region><region region-id="694" left="144" top="1467" width="99.75" height="12.75" align-x="219.75" align-y="1476" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><math optimize="false" disable-calc="false"><ml:eval><ml:apply><ml:id xml:space="preserve">percentile</ml:id><ml:sequence><ml:id xml:space="preserve">x</ml:id><ml:real>0.90</ml:real></ml:sequence></ml:apply><result xmlns="http://schemas.mathsoft.com/math20"><ml:real>9.8</ml:real></result></ml:eval></math><rendering item-idref="25" /></region><region region-id="695" left="144" top="1484.25" width="217.5" height="12" align-x="144" align-y="1494" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">because there are 11 entries in this vector.</p></text></region><region region-id="658" left="36" top="1544.25" width="303.75" height="60" align-x="36" align-y="1554" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Note that if the indexed value occurs between two data points, then we have to calculate the amount to add or subtract from an actual point in the data set to give the percentile. A quartile is one of the three percentiles that mark 1/4 of the data:</p></text></region><region region-id="659" left="66" top="1617" width="129.75" height="12.75" align-x="106.5" align-y="1626" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><math optimize="false" disable-calc="false"><ml:define><ml:id xml:space="preserve">quartile1</ml:id><ml:apply><ml:id xml:space="preserve">percentile</ml:id><ml:sequence><ml:id xml:space="preserve">mfg</ml:id><ml:real>0.25</ml:real></ml:sequence></ml:apply></ml:define></math><rendering item-idref="26" /></region><region region-id="670" left="222" top="1617" width="68.25" height="12.75" align-x="261.75" align-y="1626" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><math optimize="false" disable-calc="false"><ml:eval><ml:id xml:space="preserve">quartile1</ml:id><result xmlns="http://schemas.mathsoft.com/math20"><ml:real>67.1</ml:real></result></ml:eval></math><rendering item-idref="27" /></region><region region-id="674" left="66" top="1635" width="129.75" height="12.75" align-x="106.5" align-y="1644" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><math optimize="false" disable-calc="false"><ml:define><ml:id xml:space="preserve">quartile2</ml:id><ml:apply><ml:id xml:space="preserve">percentile</ml:id><ml:sequence><ml:id xml:space="preserve">mfg</ml:id><ml:real>0.50</ml:real></ml:sequence></ml:apply></ml:define></math><rendering item-idref="28" /></region><region region-id="673" left="222" top="1635" width="61.5" height="12.75" align-x="261.75" align-y="1644" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><math optimize="false" disable-calc="false"><ml:eval><ml:id xml:space="preserve">quartile2</ml:id><result xmlns="http://schemas.mathsoft.com/math20"><ml:real>81</ml:real></result></ml:eval></math><rendering item-idref="29" /></region><region region-id="666" left="66" top="1653" width="129.75" height="12.75" align-x="106.5" align-y="1662" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><math optimize="false" disable-calc="false"><ml:define><ml:id xml:space="preserve">quartile3</ml:id><ml:apply><ml:id xml:space="preserve">percentile</ml:id><ml:sequence><ml:id xml:space="preserve">mfg</ml:id><ml:real>0.75</ml:real></ml:sequence></ml:apply></ml:define></math><rendering item-idref="30" /></region><region region-id="672" left="222" top="1653" width="68.25" height="12.75" align-x="261.75" align-y="1662" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><math optimize="false" disable-calc="false"><ml:eval><ml:id xml:space="preserve">quartile3</ml:id><result xmlns="http://schemas.mathsoft.com/math20"><ml:real>85.5</ml:real></result></ml:eval></math><rendering item-idref="31" /></region><region region-id="678" left="36" top="1682.25" width="280.5" height="24" align-x="36" align-y="1692" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><text use-page-width="false" push-down="false" lock-width="true"><p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="144">Quartiles are best used for graphical analysis of data in <b><u><link href="./QQplot.xmcd" title="Links to section" popup="false">Quantile-Quantile plots</link></u></b>.</p></text></region><region region-id="679" left="6" top="1722" width="427.5" height="5.25" align-x="6" align-y="1722" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""><png item-idref="32" display-width="426" display-height="3.75" /><rendering item-idref="33" /></region></regions><binaryContent><item item-id="1" content-encoding="gzip">H4sIAAAAAAAA/4yNvQ6CQBCEdwEVEMXGGhMbj5InsDBWJj6CnvifEA1SWPrm5+yCvUf2mJv7
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