document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=332582>Question 332582</A>: <I><SPAN STYLE=\"word-break: break-all;\"> for the following data set, approximate the sample standard deviation.\r<BR>\n" );
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document.write( "miles (per day)---Frequency\r<BR>\n" );
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document.write( "1-2--------------- 9<BR>\n" );
document.write( "3-4--------------- 22<BR>\n" );
document.write( "5-6--------------- 28<BR>\n" );
document.write( "7-8--------------- 15<BR>\n" );
document.write( "9-10-------------- 14 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #238367 by </B><A HREF=/tutors/aboutme.mpl?userid=jrfrunner><B>jrfrunner(365)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jrfrunner><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=jrfrunner><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=238367\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Since you dont have the exact value, but instead have a range of values<BR>\n" );
document.write( "the first thing to do is to get a surrogate (proxy) value.  This is usually set a the mid point of the interval\r<BR>\n" );
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document.write( "1.5<BR>\n" );
document.write( "3.5<BR>\n" );
document.write( "etc...<BR>\n" );
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document.write( "next set up a data table as follows\r<BR>\n" );
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document.write( "Let X=midpoint, F=frequency<BR>\n" );
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document.write( "  X ------   F ----  X*F    <BR>\n" );
document.write( "1.5 -----   9 ----  13.5<BR>\n" );
document.write( "3.5 ----- 22  ----  77.0<BR>\n" );
document.write( "5.5 ----- 28  ---- 154.0<BR>\n" );
document.write( "7.5 ----- 15  ---- 112.5<BR>\n" );
document.write( "9.5 ----- 14  ---- 133.0        <BR>\n" );
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document.write( "Compute the average = Xbar = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%28Xi%2AFi%29%2Fsum%28Fi%29=490%2F88=5.57 ALIGN=MIDDLE  ALT=\"sum%28Xi%2AFi%29%2Fsum%28Fi%29=490%2F88=5.57\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "for each interval compute a column (Xi-Xbar)^2<BR>\n" );
document.write( "and then sum this column<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%28%28Xi-Xbar%29%5E2%29%2AFi ALIGN=MIDDLE  ALT=\"sum%28%28Xi-Xbar%29%5E2%29%2AFi\"   DISABLED_style= \"max-width:90%; height:auto;\" > =[(1.5-5.57)^2]*9 + [(3.5-5.57)^2]*22 +..+[(9.5-5.57)^2]*14 = 515.59\r<BR>\n" );
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document.write( "this sum represents the sum of squared deviations.<BR>\n" );
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document.write( "Find the Variance<BR>\n" );
document.write( "Variance = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sum%28%28Xi-Xbar%29%5E2%29%2AFi%2F%28sum%28Fi%29-1%29 ALIGN=MIDDLE  ALT=\"sum%28%28Xi-Xbar%29%5E2%29%2AFi%2F%28sum%28Fi%29-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=515.59/(88-1)=5.926<BR>\n" );
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document.write( "Standard dev = Sqrt(Variance) = Sqrt(5.926)=2.434\r<BR>\n" );
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document.write( "===<BR>\n" );
document.write( "There is another form of the variance formula that you could use\r<BR>\n" );
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document.write( "Variance = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sum%28%28Xi%5E2%29%29%2AFi+-+Xbar%5E2%2Asum%28Fi%29%29%2F%28sum%28Fi%29-1%29 ALIGN=MIDDLE  ALT=\"%28sum%28%28Xi%5E2%29%29%2AFi+-+Xbar%5E2%2Asum%28Fi%29%29%2F%28sum%28Fi%29-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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