document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=202195>Question 202195</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the standard deviation for the given data.\r<BR>\n" );
document.write( "\n" );
document.write( "The manager of an electrical supply store measured the diameters of the rolls of wire in the inventory. The diameters of the rolls (in m) are listed below. Round results to four decimal places.<BR>\n" );
document.write( "0.202 0.426 0.349 0.365 0.669 0.427 0.569<BR>\n" );
document.write( "A) 1.2917<BR>\n" );
document.write( "B) 1.4310<BR>\n" );
document.write( "C) 0.365<BR>\n" );
document.write( "D) 0.1523\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "I came up with like .141 or something, how do i solve this? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #152453 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=152453\">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" );
document.write( "\n" );
document.write( "0.202,0.349,0.365,0.426,0.427,0.569,0.669\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now let's find the mean. So add up all of the numbers and divide the sum by the number of numbers (which in this case is 7).\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Mean=%280.202%2B0.349%2B0.365%2B0.426%2B0.427%2B0.569%2B0.669%29%2F7=3.007%2F7=0.42957 ALIGN=MIDDLE  ALT=\"Mean=%280.202%2B0.349%2B0.365%2B0.426%2B0.427%2B0.569%2B0.669%29%2F7=3.007%2F7=0.42957\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the mean is 0.42957\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Use this formula to find the Standard Deviation:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Standard Deviation:<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE   \sigma=\sqrt{ \frac{1}{N-1}\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 average, <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" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So we can replace N with 7\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE\sqrt{ \frac{1}{7-1}\displaystyle\sum_{i=0}^7 (x_i-\bar{x})^2}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7-1 ALIGN=MIDDLE  ALT=\"7-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get 6\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE\sqrt{ \frac{1}{6}\displaystyle\sum_{i=0}^7 (x_i-\bar{x})^2}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Replace  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \bar{x}\"> with 0.42957\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE\sqrt{ \frac{1}{6}\displaystyle\sum_{i=0}^7 (x_i-0.42957)^2}\">\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
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" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%281%2F6%29%28%280.202-0.42957%29%5E2%2B%280.349-0.42957%29%5E2%2B%280.365-0.42957%29%5E2%2B%280.426-0.42957%29%5E2%2B%280.427-0.42957%29%5E2%2B%280.569-0.42957%29%5E2%2B%280.669-0.42957%29%5E2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Subtract the terms in the parenthesis\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%281%2F6%29%28%28-0.228%29%5E2%2B%28-0.081%29%5E2%2B%28-0.065%29%5E2%2B%28-0.004%29%5E2%2B%28-0.003%29%5E2%2B%280.139%29%5E2%2B%280.239%29%5E2%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Square each term\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%281%2F6%29%280.051984%2B0.006561%2B0.004225%2B0.000016%2B0.000009%2B0.019321%2B0.057121%29%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Add up all of the terms\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28%281%2F6%290.139237%29 ALIGN=MIDDLE  ALT=\"sqrt%28%281%2F6%290.139237%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Multiply\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%280.0232061666666667%29 ALIGN=MIDDLE  ALT=\"sqrt%280.0232061666666667%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Take the square root\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.152335703847347 ALIGN=MIDDLE  ALT=\"0.152335703847347\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the standard deviation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.152335703847347 ALIGN=MIDDLE  ALT=\"0.152335703847347\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "which rounds to 0.1523\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So the answer is D) 0.1523 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );