document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193598>Question 1193598</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A sample of 12 measurements has a mean of 31 and a standard deviation of 4.75. Suppose that the sample is enlarged to 14 measurements, by including two additional measurements having a common value of 31 each.\r<BR>\n" );
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document.write( "Find the standard deviation of the sample of 14 measurements. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #825685 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=825685\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the variance is the sum of the squared deviations divided by (n-1)<BR>\n" );
document.write( "so sd is sqrt(SSD/n-1)=4.75<BR>\n" );
document.write( "and  22.5625(n-1)=SSD=22.5625*11=248.1875<BR>\n" );
document.write( "There is the same sum of squared deviations with two more values added that are exactly 31, so now the variance is 248.1875/13=19.09<BR>\n" );
document.write( "that makes the sd=4.37<BR>\n" );
document.write( "this is essentially multiplying the original sd by the ratio of the sqrt of the old sample size-1/new one-1, since sd is proportional to the inverse square of n-1 for samples.  4.75*sqrt(11)/sqrt(13)=4.37 </SPAN>\n" );
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