document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1133608>Question 1133608</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the sample standard deviation.\r<BR>\n" );
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document.write( "22 29 21 24 27 28 25 36 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #750857 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=750857\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "Standard Deviation,\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=22 ALIGN=MIDDLE  ALT=\"22\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=29 ALIGN=MIDDLE  ALT=\"29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21 ALIGN=MIDDLE  ALT=\"21\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24 ALIGN=MIDDLE  ALT=\"24\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27 ALIGN=MIDDLE  ALT=\"27\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28 ALIGN=MIDDLE  ALT=\"28\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25 ALIGN=MIDDLE  ALT=\"25\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36 ALIGN=MIDDLE  ALT=\"36\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "First, work out the average, or arithmetic mean, of the numbers:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu=%2822%2B29%2B21%2B24%2B27%2B28%2B25+%2B36%29%2F8=26.5 ALIGN=MIDDLE  ALT=\"mu=%2822%2B29%2B21%2B24%2B27%2B28%2B25+%2B36%29%2F8=26.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N+=8 ALIGN=MIDDLE  ALT=\"N+=8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Then, take each number, subtract the mean and square the result:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=22-26.5=-4.5 ALIGN=MIDDLE  ALT=\"22-26.5=-4.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=29-26.5=2.5 ALIGN=MIDDLE  ALT=\"29-26.5=2.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21-26.5=-5.5 ALIGN=MIDDLE  ALT=\"21-26.5=-5.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24-26.5=-2.5 ALIGN=MIDDLE  ALT=\"24-26.5=-2.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27-26.5=0.5 ALIGN=MIDDLE  ALT=\"27-26.5=0.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28-26.5=1.5 ALIGN=MIDDLE  ALT=\"28-26.5=1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=25+-26.5=-1.5 ALIGN=MIDDLE  ALT=\"25+-26.5=-1.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36-26.5=+9.5 ALIGN=MIDDLE  ALT=\"36-26.5=+9.5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Square of each difference:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-4.5%29%5E2 ALIGN=MIDDLE  ALT=\"%28-4.5%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.5%5E2 ALIGN=MIDDLE  ALT=\"2.5%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-5.5%29%5E2 ALIGN=MIDDLE  ALT=\"+%28-5.5%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-2.5%29%5E2 ALIGN=MIDDLE  ALT=\"%28-2.5%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0.5%5E2 ALIGN=MIDDLE  ALT=\"+0.5%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.5%5E2 ALIGN=MIDDLE  ALT=\"1.5%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28-1.5%29%5E2 ALIGN=MIDDLE  ALT=\"+%28-1.5%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9.5%5E2 ALIGN=MIDDLE  ALT=\"9.5%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20.25 ALIGN=MIDDLE  ALT=\"20.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6.25 ALIGN=MIDDLE  ALT=\"6.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30.25 ALIGN=MIDDLE  ALT=\"30.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6.25 ALIGN=MIDDLE  ALT=\"+6.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.25 ALIGN=MIDDLE  ALT=\"0.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.25 ALIGN=MIDDLE  ALT=\"2.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.25 ALIGN=MIDDLE  ALT=\"2.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90.25 ALIGN=MIDDLE  ALT=\"90.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now calculate the Variance:\r<BR>\n" );
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document.write( "add up the squared differences and divide by count\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2820.25%2B6.25%2B30.25%2B+6.25%2B+0.25%2B+2.25%2B+2.25%2B90.25%29%2F8=158%2F8=19.75 ALIGN=MIDDLE  ALT=\"%2820.25%2B6.25%2B30.25%2B+6.25%2B+0.25%2B+2.25%2B+2.25%2B90.25%29%2F8=158%2F8=19.75\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Lastly, take the square root of the Variance: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2819.75%29=4.444097209 ALIGN=MIDDLE  ALT=\"sqrt%2819.75%29=4.444097209\"   DISABLED_style= \"max-width:90%; height:auto;\" >->the sample standard deviation\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );