document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=477232>Question 477232</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the range, standard deviation, and variance for the following sample data:<BR>\n" );
document.write( "33, 55, 29, 40, 43, 8, 90, 61, 41, 17, 80, 56, 17, 59, 21, 78 \r<BR>\n" );
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document.write( "Thank you \r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #327145 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=327145\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Range = Largest Value - Smallest Value\r<BR>\n" );
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document.write( "Range = 90 - 8\r<BR>\n" );
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document.write( "Range = 82\r<BR>\n" );
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document.write( "Finding the sample variance and 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 = (33+55+29+40+43+8+90+61+41+17+80+56+17+59+21+78)/16 = 728/16 = 45.5 \r<BR>\n" );
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document.write( "So the sample mean is xbar = 45.5 \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( "33-45.5 = -12.5<BR>\n" );
document.write( "55-45.5 = 9.5<BR>\n" );
document.write( "29-45.5 = -16.5<BR>\n" );
document.write( "40-45.5 = -5.5<BR>\n" );
document.write( "43-45.5 = -2.5<BR>\n" );
document.write( "8-45.5 = -37.5<BR>\n" );
document.write( "90-45.5 = 44.5<BR>\n" );
document.write( "61-45.5 = 15.5<BR>\n" );
document.write( "41-45.5 = -4.5<BR>\n" );
document.write( "17-45.5 = -28.5<BR>\n" );
document.write( "80-45.5 = 34.5<BR>\n" );
document.write( "56-45.5 = 10.5<BR>\n" );
document.write( "17-45.5 = -28.5<BR>\n" );
document.write( "59-45.5 = 13.5<BR>\n" );
document.write( "21-45.5 = -24.5<BR>\n" );
document.write( "78-45.5 = 32.5\r<BR>\n" );
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document.write( "So the differences are: -12.5, 9.5, -16.5, -5.5, -2.5, -37.5, 44.5, 15.5, -4.5, -28.5, 34.5, 10.5, -28.5, 13.5, -24.5, 32.5 \r<BR>\n" );
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document.write( "Now square each difference:\r<BR>\n" );
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document.write( "(-12.5)^2 = 156.25<BR>\n" );
document.write( "(9.5)^2 = 90.25<BR>\n" );
document.write( "(-16.5)^2 = 272.25<BR>\n" );
document.write( "(-5.5)^2 = 30.25<BR>\n" );
document.write( "(-2.5)^2 = 6.25<BR>\n" );
document.write( "(-37.5)^2 = 1406.25<BR>\n" );
document.write( "(44.5)^2 = 1980.25<BR>\n" );
document.write( "(15.5)^2 = 240.25<BR>\n" );
document.write( "(-4.5)^2 = 20.25<BR>\n" );
document.write( "(-28.5)^2 = 812.25<BR>\n" );
document.write( "(34.5)^2 = 1190.25<BR>\n" );
document.write( "(10.5)^2 = 110.25<BR>\n" );
document.write( "(-28.5)^2 = 812.25<BR>\n" );
document.write( "(13.5)^2 = 182.25<BR>\n" );
document.write( "(-24.5)^2 = 600.25<BR>\n" );
document.write( "(32.5)^2 = 1056.25\r<BR>\n" );
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document.write( "Now add up each square:\r<BR>\n" );
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document.write( "156.25+90.25+272.25+30.25+6.25+1406.25+1980.25+240.25+20.25+812.25+1190.25+110.25+812.25+182.25+600.25+1056.25 = 8966\r<BR>\n" );
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document.write( "Now divide that sum by n-1 = 16-1 = 15 to get 8966/15 = 597.733333333333\r<BR>\n" );
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document.write( "So the sample variance is 597.733333333333\r<BR>\n" );
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document.write( "Finally, take the square root of 597.733333333333 to get 24.448585507823\r<BR>\n" );
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document.write( "So the sample standard deviation is 24.448585507823\r<BR>\n" );
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