document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=6528>Question 6528</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do I find the standard deviation to the nearest tenth of the following set of data? {47, 61, 93, 22, 82, 22, 37} </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #3540 by </B><A HREF=/tutors/aboutme.mpl?userid=Mike><B>Mike(39)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Mike><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=3540\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Firstly, there are two different types of standard deviation - population standard deviation and sample standard deviation. I assume you are trying to find the population standard deviation, because that is the most common.\r<BR>\n" );
document.write( "\n" );
document.write( "In order to find the population standard deviation without the use of a calculator, you need to first establish the mean(µ) of your set of data. The µ of your set of data is: 52. You must now establish how much each one of your marks(M) deviates from the µ (i.e. 47 - 52, 61 - 52, etc. etc.). You then square that deviation and multiply it by the frequency (f) of that mark(M) (the entire formula for this procedure is f(M-µ)^2). Let me show you what I mean:\r<BR>\n" );
document.write( "\n" );
document.write( "1) 47 - 52 = -5<BR>\n" );
document.write( "2) -5^2 = 25<BR>\n" );
document.write( "3) f is equal to 1 because it only appears once in your set of data.<BR>\n" );
document.write( "Therefore, in this case, f(M-µ)^2) = 1(47-52)^2 = 25\r<BR>\n" );
document.write( "\n" );
document.write( "For the others:<BR>\n" );
document.write( "1(61-52)^2 = 81<BR>\n" );
document.write( "1(93-52)^2 = 1681<BR>\n" );
document.write( "2(22-52)^2 = 1800<BR>\n" );
document.write( "1(82-52)^2 = 900<BR>\n" );
document.write( "1(37-52)^2 = 225\r<BR>\n" );
document.write( "\n" );
document.write( "You now add all of these answers up and divide them by the number of data points you have (7 in this case: 47, 61, 93, 22, 82, 22, 37)\r<BR>\n" );
document.write( "\n" );
document.write( "25+81+1681+1800+900+225 = 4712/7 = 673.14. This is known as the Variance.<BR>\n" );
document.write( "In order to obtain the population standard deviation, all you now need to do is take the square root of the variance. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28+673.14+%29 ALIGN=MIDDLE  ALT=\"sqrt%28+673.14+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 25.94\r<BR>\n" );
document.write( "\n" );
document.write( "This entire procedure is a whole lot easier to do if you have a graphing calculator like the Ti-83, but being dependent on your calculator is never a good thing.<BR>\n" );
document.write( "If you have any more questions let me know.<BR>\n" );
document.write( "Regards,<BR>\n" );
document.write( "-Mike </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );