document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=888698>Question 888698</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Can someone help with the following:\r<BR>\n" );
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document.write( "In her first year of university, Mary received the following grades:\r<BR>\n" );
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document.write( "12, 8, 12, 11, 9, 6\r<BR>\n" );
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document.write( "Similarly in his first year, Bob received the following grades:\r<BR>\n" );
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document.write( "5, 9, 9, 6, 5, 7\r<BR>\n" );
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document.write( "Compute the population mean and variance for both.\r<BR>\n" );
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document.write( "My Work:\r<BR>\n" );
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document.write( "Mary's mean 9.67<BR>\n" );
document.write( "Bob's mean 6.83\r<BR>\n" );
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document.write( "not sure of the variance\r<BR>\n" );
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document.write( "thanks Paul<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 #537604 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=537604\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> sum of squares for mary is 29.33<BR>\n" );
document.write( "sum of squares for bob is 16.83\r<BR>\n" );
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document.write( "the population variance for mary is 4.89<BR>\n" );
document.write( "the population variance for bob is 2.81\r<BR>\n" );
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document.write( "the population variance is equal to the sum of squares divided by the count of the number of items.\r<BR>\n" );
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document.write( "for mary, this would be 29.33 / 6 = 4.89<BR>\n" );
document.write( "for bob, this would be 16.83 / 6 = 2.81\r<BR>\n" );
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document.write( "the sum of squares can be calculated in two basic ways.\r<BR>\n" );
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document.write( "first way is:\r<BR>\n" );
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document.write( "sum of squares = sum of (x-m)^2, where x is the individual data values and m is the mean of the data set.\r<BR>\n" );
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document.write( "second way is:\r<BR>\n" );
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document.write( "sum of squares = sum of (x^2) - (sum of x)^2 / n, where x is the individual data values and n is the count of data items.\r<BR>\n" );
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document.write( "both these methods are shown in the excel spreadsheet under sum of squares option 1 and sum of squares option 2.\r<BR>\n" );
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document.write( "sum of squares option 3 is equal to the population variance * the count of items.<BR>\n" );
document.write( "this can be done in excel because excel provides a formula for variance and a formula for count but does not provide a direct formula for sum of squares, so you can get the sum of squares through excel by multiplying the population variation by the count of items.\r<BR>\n" );
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document.write( "the calculations are shown in the following picture of an excel spreadsheet.<BR>\n" );
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