document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=117072>Question 117072</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the standard deviation of <BR>\n" );
document.write( "75 77 78 78 79 80 80 81 84 85 87 89 90 91\r<BR>\n" );
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document.write( "HELP </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #85132 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=85132\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First sort the numbers into ascending order (from least to greatest):\r<BR>\n" );
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document.write( "75,77,78,78,79,80,80,81,84,85,87,89,90,91\r<BR>\n" );
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document.write( "Now we need the mean. So add up all of the numbers and divide the sum by the number of numbers (which in this case is 14).\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Mean=%2875%2B77%2B78%2B78%2B79%2B80%2B80%2B81%2B84%2B85%2B87%2B89%2B90%2B91%29%2F14=1154%2F14=82.4285714285714 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the mean is 82.4285714285714\r<BR>\n" );
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document.write( "Now that we have the mean, we can use this formula to find the standard deviation:\r<BR>\n" );
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document.write( "Standard Deviation:<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE  \sigma=\sqrt{ \frac{1}{N}\displaystyle\sum_{i=0}^N (x_i-\bar{x})^2}\"> where <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \bar{x}\"> is the arithmetic mean, <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x_i\"> is the ith number, and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE N\"> is the number of numbers\r<BR>\n" );
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document.write( "So we can replace N with 14\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE\sqrt{ \frac{1}{14}\displaystyle\sum_{i=0}^{14} (x_i-\bar{x})^2}\">\r<BR>\n" );
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document.write( "Replace  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \bar{x}\"> with 82.4285714285714\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE\sqrt{ \frac{1}{14}\displaystyle\sum_{i=0}^{14} (x_i-82.4285714285714)^2}\">\r<BR>\n" );
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document.write( "Expand the summation (replace each <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5Bi%5D ALIGN=MIDDLE  ALT=\"x%5Bi%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > with the respective number)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%281%2F14%29%28%2875-82.4285714285714%29%5E2%2B%2877-82.4285714285714%29%5E2%2B%2878-82.4285714285714%29%5E2%2B%2878-82.4285714285714%29%5E2%2B%2879-82.4285714285714%29%5E2%2B%2880-82.4285714285714%29%5E2%2B%2880-82.4285714285714%29%5E2%2B%2881-82.4285714285714%29%5E2%2B%2884-82.4285714285714%29%5E2%2B%2885-82.4285714285714%29%5E2%2B%2887-82.4285714285714%29%5E2%2B%2889-82.4285714285714%29%5E2%2B%2890-82.4285714285714%29%5E2%2B%2891-82.4285714285714%29%5E2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Subtract the terms in the parenthesis\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%281%2F14%29%28%28-7.429%29%5E2%2B%28-5.429%29%5E2%2B%28-4.429%29%5E2%2B%28-4.429%29%5E2%2B%28-3.429%29%5E2%2B%28-2.429%29%5E2%2B%28-2.429%29%5E2%2B%28-1.429%29%5E2%2B%281.571%29%5E2%2B%282.571%29%5E2%2B%284.571%29%5E2%2B%286.571%29%5E2%2B%287.571%29%5E2%2B%288.571%29%5E2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Square each term\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%281%2F14%29%2855.190041%2B29.474041%2B19.616041%2B19.616041%2B11.758041%2B5.900041%2B5.900041%2B2.042041%2B2.468041%2B6.610041%2B20.894041%2B43.178041%2B57.320041%2B73.462041%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Add up all of the terms\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%281%2F14%29353.428574%29 ALIGN=MIDDLE  ALT=\"sqrt%28%281%2F14%29353.428574%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2825.2448981428571%29 ALIGN=MIDDLE  ALT=\"sqrt%2825.2448981428571%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Take the square root\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5.02443013115489 ALIGN=MIDDLE  ALT=\"5.02443013115489\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the standard deviation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5.02443013115489 ALIGN=MIDDLE  ALT=\"5.02443013115489\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Here is an <a  rel=nofollow HREF=http://www.csgnetwork.com/stddeviationcalc.html>online standard deviation calculator</a> that will check your work.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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