document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=476935>Question 476935</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Need help with this problem: Find the rand,standard deviation,and variance for the following sample data: 77,67,5,30,19,79,9,23,1,51,56,82,27,1,9,90 not really sure how to do any part of this need step by step if at all possible please and thank you!!!!!!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #326975 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=326975\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Not familiar with the term \"rand\". Is that a typo?\r<BR>\n" );
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document.write( "Finding the sample standard deviation:\r<BR>\n" );
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document.write( "First, we need to find the sample mean xbar\r<BR>\n" );
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document.write( "xbar = (77+67+5+30+19+79+9+23+1+51+56+82+27+1+9+90)/16 = 626/16 = 39.125 \r<BR>\n" );
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document.write( "So the sample mean is xbar = 39.125 \r<BR>\n" );
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document.write( "Now subtract the sample mean from EVERY data value:\r<BR>\n" );
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document.write( "77-39.125 = 37.875<BR>\n" );
document.write( "67-39.125 = 27.875<BR>\n" );
document.write( "5-39.125 = -34.125<BR>\n" );
document.write( "30-39.125 = -9.125<BR>\n" );
document.write( "19-39.125 = -20.125<BR>\n" );
document.write( "79-39.125 = 39.875<BR>\n" );
document.write( "9-39.125 = -30.125<BR>\n" );
document.write( "23-39.125 = -16.125<BR>\n" );
document.write( "1-39.125 = -38.125<BR>\n" );
document.write( "51-39.125 = 11.875<BR>\n" );
document.write( "56-39.125 = 16.875<BR>\n" );
document.write( "82-39.125 = 42.875<BR>\n" );
document.write( "27-39.125 = -12.125<BR>\n" );
document.write( "1-39.125 = -38.125<BR>\n" );
document.write( "9-39.125 = -30.125<BR>\n" );
document.write( "90-39.125 = 50.875\r<BR>\n" );
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document.write( "So the differences are: 37.875, 27.875, -34.125, -9.125, -20.125, 39.875, -30.125, -16.125, -38.125, 11.875, 16.875, 42.875, -12.125, -38.125, -30.125, 50.875 \r<BR>\n" );
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document.write( "Now square each difference:\r<BR>\n" );
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document.write( "(37.875)^2 = 1434.515625<BR>\n" );
document.write( "(27.875)^2 = 777.015625<BR>\n" );
document.write( "(-34.125)^2 = 1164.515625<BR>\n" );
document.write( "(-9.125)^2 = 83.265625<BR>\n" );
document.write( "(-20.125)^2 = 405.015625<BR>\n" );
document.write( "(39.875)^2 = 1590.015625<BR>\n" );
document.write( "(-30.125)^2 = 907.515625<BR>\n" );
document.write( "(-16.125)^2 = 260.015625<BR>\n" );
document.write( "(-38.125)^2 = 1453.515625<BR>\n" );
document.write( "(11.875)^2 = 141.015625<BR>\n" );
document.write( "(16.875)^2 = 284.765625<BR>\n" );
document.write( "(42.875)^2 = 1838.265625<BR>\n" );
document.write( "(-12.125)^2 = 147.015625<BR>\n" );
document.write( "(-38.125)^2 = 1453.515625<BR>\n" );
document.write( "(-30.125)^2 = 907.515625<BR>\n" );
document.write( "(50.875)^2 = 2588.265625\r<BR>\n" );
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document.write( "Now add up each square:\r<BR>\n" );
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document.write( "1434.515625+777.015625+1164.515625+83.265625+405.015625+1590.015625+907.515625+260.015625+1453.515625+141.015625+284.765625+1838.265625+147.015625+1453.515625+907.515625+2588.265625 = 15435.75\r<BR>\n" );
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document.write( "Now divide that sum by n-1 = 16-1 = 15 to get 15435.75/15 = 1029.05 \r<BR>\n" );
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document.write( "Finally, take the square root of 1029.05 to get 32.0788092048318\r<BR>\n" );
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document.write( "So the sample standard deviation is 32.0788092048318\r<BR>\n" );
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document.write( "Now simply square this value to get the sample variance (32.0788092048318)^2 = 1029.05\r<BR>\n" );
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document.write( "So the sample variance is 1029.05 </SPAN>\n" );
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