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<p class=3DMsoNormal style=3D'tab-stops:right 6.0in'><b style=3D'mso-bidi-f=
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normal'><span style=3D'font-size:14.0pt'>Measures of Variation Project<span
style=3D'mso-tab-count:1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&=
nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbs=
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1'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
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<p class=3DMsoNormal>Measures of variation reflect the amount of
&#8220;scatter&#8221; of a set of data.<span style=3D'mso-spacerun:yes'>&nb=
sp;
</span>The more &#8220;scattered&#8221; the data, the larger the measures of
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ommon
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text .5pt;
  padding:0in 5.4pt 0in 5.4pt;height:.2in'>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><o:p>&nbs=
p;</o:p></p>
  </td>
  <td width=3D144 style=3D'width:1.5in;border-top:none;border-left:none;bor=
der-bottom:
  solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;mso-border-top=
-alt:
  solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;mso-borde=
r-alt:
  solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt;height:.2in'>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><o:p>&nbs=
p;</o:p></p>
  </td>
  <td width=3D144 style=3D'width:1.5in;border-top:none;border-left:none;bor=
der-bottom:
  solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;mso-border-top=
-alt:
  solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;mso-borde=
r-alt:
  solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt;height:.2in'>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><span
  style=3D'background:yellow;mso-highlight:yellow'><o:p>&nbsp;</o:p></span>=
</p>
  </td>
 </tr>
 <tr style=3D'mso-yfti-irow:5;height:.2in'>
  <td width=3D144 style=3D'width:1.5in;border:solid windowtext 1.0pt;border=
-top:
  none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid window=
text .5pt;
  padding:0in 5.4pt 0in 5.4pt;height:.2in'>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><o:p>&nbs=
p;</o:p></p>
  </td>
  <td width=3D144 style=3D'width:1.5in;border-top:none;border-left:none;bor=
der-bottom:
  solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;mso-border-top=
-alt:
  solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;mso-borde=
r-alt:
  solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt;height:.2in'>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><o:p>&nbs=
p;</o:p></p>
  </td>
  <td width=3D144 style=3D'width:1.5in;border-top:none;border-left:none;bor=
der-bottom:
  solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;mso-border-top=
-alt:
  solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;mso-borde=
r-alt:
  solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt;height:.2in'>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><span
  style=3D'background:yellow;mso-highlight:yellow'><o:p>&nbsp;</o:p></span>=
</p>
  </td>
 </tr>
 <tr style=3D'mso-yfti-irow:6;height:.2in'>
  <td width=3D144 style=3D'width:1.5in;border:solid windowtext 1.0pt;border=
-top:
  none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid window=
text .5pt;
  padding:0in 5.4pt 0in 5.4pt;height:.2in'>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><o:p>&nbs=
p;</o:p></p>
  </td>
  <td width=3D144 style=3D'width:1.5in;border-top:none;border-left:none;bor=
der-bottom:
  solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;mso-border-top=
-alt:
  solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;mso-borde=
r-alt:
  solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt;height:.2in'>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><o:p>&nbs=
p;</o:p></p>
  </td>
  <td width=3D144 style=3D'width:1.5in;border-top:none;border-left:none;bor=
der-bottom:
  solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;mso-border-top=
-alt:
  solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;mso-borde=
r-alt:
  solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt;height:.2in'>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><span
  style=3D'background:yellow;mso-highlight:yellow'><o:p>&nbsp;</o:p></span>=
</p>
  </td>
 </tr>
 <tr style=3D'mso-yfti-irow:7;height:.2in'>
  <td width=3D144 style=3D'width:1.5in;border:solid windowtext 1.0pt;border=
-top:
  none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid window=
text .5pt;
  padding:0in 5.4pt 0in 5.4pt;height:.2in'>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><o:p>&nbs=
p;</o:p></p>
  </td>
  <td width=3D144 style=3D'width:1.5in;border-top:none;border-left:none;bor=
der-bottom:
  solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;mso-border-top=
-alt:
  solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;mso-borde=
r-alt:
  solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt;height:.2in'>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><o:p>&nbs=
p;</o:p></p>
  </td>
  <td width=3D144 style=3D'width:1.5in;border-top:none;border-left:none;bor=
der-bottom:
  solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;mso-border-top=
-alt:
  solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;mso-borde=
r-alt:
  solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt;height:.2in'>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><span
  style=3D'background:yellow;mso-highlight:yellow'><o:p>&nbsp;</o:p></span>=
</p>
  </td>
 </tr>
 <tr style=3D'mso-yfti-irow:8;mso-yfti-lastrow:yes;height:.2in'>
  <td width=3D144 style=3D'width:1.5in;border:solid windowtext 1.0pt;border=
-top:
  none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid window=
text .5pt;
  padding:0in 5.4pt 0in 5.4pt;height:.2in'>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'>Total</p>
  </td>
  <td width=3D144 style=3D'width:1.5in;border-top:none;border-left:none;bor=
der-bottom:
  solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;mso-border-top=
-alt:
  solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;mso-borde=
r-alt:
  solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt;height:.2in'>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><o:p>&nbs=
p;</o:p></p>
  </td>
  <td width=3D144 style=3D'width:1.5in;border-top:none;border-left:none;bor=
der-bottom:
  solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;mso-border-top=
-alt:
  solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;mso-borde=
r-alt:
  solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt;height:.2in'>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><span
  style=3D'background:yellow;mso-highlight:yellow'><o:p>&nbsp;</o:p></span>=
</p>
  </td>
 </tr>
</table>

<p class=3DMsoNormal style=3D'margin-left:.5in;text-indent:-.5in'><i
style=3D'mso-bidi-font-style:normal'><o:p>&nbsp;</o:p></i></p>

<p class=3DMsoNormal><b><span style=3D'font-size:14.0pt;mso-bidi-font-size:=
16.0pt'>Example:</span></b><span
style=3D'mso-spacerun:yes'>&nbsp; </span>Following is a sample of exam scor=
es for
an English class.<span style=3D'mso-spacerun:yes'>&nbsp; </span>Find the sa=
mple
standard deviation.</p>

<p class=3DMsoNormal style=3D'margin-left:.5in;text-indent:-.5in'><o:p>&nbs=
p;</o:p></p>

<p class=3DMsoHeader style=3D'margin-left:.5in;tab-stops:.5in'>Sample of Sc=
ores:
{82, 83, 84, 84, 85, 86, 86, 99)</p>

<p class=3DMsoNormal style=3D'margin-left:.5in;text-indent:-.5in'><o:p>&nbs=
p;</o:p></p>

<table class=3DMsoTableGrid border=3D1 cellspacing=3D0 cellpadding=3D0
 style=3D'border-collapse:collapse;border:none;mso-border-alt:solid windowt=
ext .5pt;
 mso-yfti-tbllook:480;mso-padding-alt:0in 5.4pt 0in 5.4pt;mso-border-inside=
h:
 .5pt solid windowtext;mso-border-insidev:.5pt solid windowtext'>
 <tr style=3D'mso-yfti-irow:0;mso-yfti-firstrow:yes'>
  <td width=3D144 style=3D'width:1.5in;border:solid windowtext 1.0pt;mso-bo=
rder-alt:
  solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt'>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><b
  style=3D'mso-bidi-font-weight:normal'><span style=3D'font-size:16.0pt'>Ob=
servation<o:p></o:p></span></b></p>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><b
  style=3D'mso-bidi-font-weight:normal'><i style=3D'mso-bidi-font-style:nor=
mal'><span
  style=3D'font-size:16.0pt'>x<o:p></o:p></span></i></b></p>
  </td>
  <td width=3D144 style=3D'width:1.5in;border:solid windowtext 1.0pt;border=
-left:
  none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:solid windo=
wtext .5pt;
  padding:0in 5.4pt 0in 5.4pt'>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><b
  style=3D'mso-bidi-font-weight:normal'><span style=3D'font-size:16.0pt'>De=
viation<o:p></o:p></span></b></p>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><b
  style=3D'mso-bidi-font-weight:normal'><i style=3D'mso-bidi-font-style:nor=
mal'><span
  style=3D'font-size:16.0pt'>x</span></i></b><b style=3D'mso-bidi-font-weig=
ht:normal'><span
  style=3D'font-size:16.0pt'> &#8211; <sub><!--[if gte vml 1]><v:shape id=
=3D"_x0000_i1027"
   type=3D"#_x0000_t75" style=3D'width:11.25pt;height:12.75pt' o:ole=3D"">
   <v:imagedata src=3D"Chapter13Project2_files/image001.wmz" o:title=3D""/>
  </v:shape><![endif]--><![if !vml]><img width=3D15 height=3D17
  src=3D"Chapter13Project2_files/image002.gif" v:shapes=3D"_x0000_i1027"><!=
[endif]></sub><!--[if gte mso 9]><xml>
   <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i102=
7"
    DrawAspect=3D"Content" ObjectID=3D"_1191165338">
   </o:OLEObject>
  </xml><![endif]--><o:p></o:p></span></b></p>
  </td>
  <td width=3D144 valign=3Dtop style=3D'width:1.5in;border:solid windowtext=
 1.0pt;
  border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt:
  solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt'>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><b
  style=3D'mso-bidi-font-weight:normal'><span style=3D'font-size:16.0pt'>(D=
eviations)<sup>2</sup><o:p></o:p></span></b></p>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><b
  style=3D'mso-bidi-font-weight:normal'><span style=3D'font-size:16.0pt'>(<i
  style=3D'mso-bidi-font-style:normal'>x</i> &#8211; </span></b><sub><!--[i=
f gte vml 1]><v:shape
   id=3D"_x0000_i1028" type=3D"#_x0000_t75" style=3D'width:11.25pt;height:1=
2.75pt'
   o:ole=3D"">
   <v:imagedata src=3D"Chapter13Project2_files/image001.wmz" o:title=3D""/>
  </v:shape><![endif]--><![if !vml]><img width=3D15 height=3D17
  src=3D"Chapter13Project2_files/image002.gif" v:shapes=3D"_x0000_i1028"><!=
[endif]></sub><!--[if gte mso 9]><xml>
   <o:OLEObject Type=3D"Embed" ProgID=3D"Equation.3" ShapeID=3D"_x0000_i102=
8"
    DrawAspect=3D"Content" ObjectID=3D"_1191165339">
   </o:OLEObject>
  </xml><![endif]-->)<sup>2</sup><b style=3D'mso-bidi-font-weight:normal'><=
span
  style=3D'font-size:16.0pt'><o:p></o:p></span></b></p>
  </td>
 </tr>
 <tr style=3D'mso-yfti-irow:1;height:.2in'>
  <td width=3D144 style=3D'width:1.5in;border:solid windowtext 1.0pt;border=
-top:
  none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid window=
text .5pt;
  padding:0in 5.4pt 0in 5.4pt;height:.2in'>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><o:p>&nbs=
p;</o:p></p>
  </td>
  <td width=3D144 style=3D'width:1.5in;border-top:none;border-left:none;bor=
der-bottom:
  solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;mso-border-top=
-alt:
  solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;mso-borde=
r-alt:
  solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt;height:.2in'>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><o:p>&nbs=
p;</o:p></p>
  </td>
  <td width=3D144 style=3D'width:1.5in;border-top:none;border-left:none;bor=
der-bottom:
  solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;mso-border-top=
-alt:
  solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;mso-borde=
r-alt:
  solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt;height:.2in'>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><span
  style=3D'background:yellow;mso-highlight:yellow'><o:p>&nbsp;</o:p></span>=
</p>
  </td>
 </tr>
 <tr style=3D'mso-yfti-irow:2;height:.2in'>
  <td width=3D144 style=3D'width:1.5in;border:solid windowtext 1.0pt;border=
-top:
  none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid window=
text .5pt;
  padding:0in 5.4pt 0in 5.4pt;height:.2in'>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><o:p>&nbs=
p;</o:p></p>
  </td>
  <td width=3D144 style=3D'width:1.5in;border-top:none;border-left:none;bor=
der-bottom:
  solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;mso-border-top=
-alt:
  solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;mso-borde=
r-alt:
  solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt;height:.2in'>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><o:p>&nbs=
p;</o:p></p>
  </td>
  <td width=3D144 style=3D'width:1.5in;border-top:none;border-left:none;bor=
der-bottom:
  solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;mso-border-top=
-alt:
  solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;mso-borde=
r-alt:
  solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt;height:.2in'>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><span
  style=3D'background:yellow;mso-highlight:yellow'><o:p>&nbsp;</o:p></span>=
</p>
  </td>
 </tr>
 <tr style=3D'mso-yfti-irow:3;height:.2in'>
  <td width=3D144 style=3D'width:1.5in;border:solid windowtext 1.0pt;border=
-top:
  none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid window=
text .5pt;
  padding:0in 5.4pt 0in 5.4pt;height:.2in'>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><o:p>&nbs=
p;</o:p></p>
  </td>
  <td width=3D144 style=3D'width:1.5in;border-top:none;border-left:none;bor=
der-bottom:
  solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;mso-border-top=
-alt:
  solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;mso-borde=
r-alt:
  solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt;height:.2in'>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><o:p>&nbs=
p;</o:p></p>
  </td>
  <td width=3D144 style=3D'width:1.5in;border-top:none;border-left:none;bor=
der-bottom:
  solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;mso-border-top=
-alt:
  solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;mso-borde=
r-alt:
  solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt;height:.2in'>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><span
  style=3D'background:yellow;mso-highlight:yellow'><o:p>&nbsp;</o:p></span>=
</p>
  </td>
 </tr>
 <tr style=3D'mso-yfti-irow:4;height:.2in'>
  <td width=3D144 style=3D'width:1.5in;border:solid windowtext 1.0pt;border=
-top:
  none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid window=
text .5pt;
  padding:0in 5.4pt 0in 5.4pt;height:.2in'>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><o:p>&nbs=
p;</o:p></p>
  </td>
  <td width=3D144 style=3D'width:1.5in;border-top:none;border-left:none;bor=
der-bottom:
  solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;mso-border-top=
-alt:
  solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;mso-borde=
r-alt:
  solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt;height:.2in'>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><o:p>&nbs=
p;</o:p></p>
  </td>
  <td width=3D144 style=3D'width:1.5in;border-top:none;border-left:none;bor=
der-bottom:
  solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;mso-border-top=
-alt:
  solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;mso-borde=
r-alt:
  solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt;height:.2in'>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><span
  style=3D'background:yellow;mso-highlight:yellow'><o:p>&nbsp;</o:p></span>=
</p>
  </td>
 </tr>
 <tr style=3D'mso-yfti-irow:5;height:.2in'>
  <td width=3D144 style=3D'width:1.5in;border:solid windowtext 1.0pt;border=
-top:
  none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid window=
text .5pt;
  padding:0in 5.4pt 0in 5.4pt;height:.2in'>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><o:p>&nbs=
p;</o:p></p>
  </td>
  <td width=3D144 style=3D'width:1.5in;border-top:none;border-left:none;bor=
der-bottom:
  solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;mso-border-top=
-alt:
  solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;mso-borde=
r-alt:
  solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt;height:.2in'>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><o:p>&nbs=
p;</o:p></p>
  </td>
  <td width=3D144 style=3D'width:1.5in;border-top:none;border-left:none;bor=
der-bottom:
  solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;mso-border-top=
-alt:
  solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;mso-borde=
r-alt:
  solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt;height:.2in'>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><span
  style=3D'background:yellow;mso-highlight:yellow'><o:p>&nbsp;</o:p></span>=
</p>
  </td>
 </tr>
 <tr style=3D'mso-yfti-irow:6;height:.2in'>
  <td width=3D144 style=3D'width:1.5in;border:solid windowtext 1.0pt;border=
-top:
  none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid window=
text .5pt;
  padding:0in 5.4pt 0in 5.4pt;height:.2in'>
  <p class=3DMsoNormal align=3Dcenter style=3D'text-align:center'><o:p>&nbs=
p;</o:p></p>
  </td>
  <td width=3D144 style=3D'width:1.5in;border-top:none;border-left:none;bor=
der-bottom:
  solid windowtext 1.0pt;border-right:solid windowtext 1.0pt;mso-border-top=
-alt:
  solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt;mso-borde=
r-alt:
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