document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=20536>Question 20536</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need to construct a set of twelve numbers with a mean of 7 a median of 6 and a mode of 8.  Can you help.\r<BR>\n" );
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document.write( "Teri </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #9888 by </B><A HREF=/tutors/aboutme.mpl?userid=venugopalramana><B>venugopalramana(3286)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=venugopalramana><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.geocities.com/venugopalramana/FREE_MATHS_ASSISTANCE.html valign=middle><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=9888\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> there are 12 numbers..say x1,x2,x3,.....x11,x12 when arranged in increasing order.<BR>\n" );
document.write( "mean is 7.so sum of numbers by /total no.of numbers=7=(x1+x2+....+x11+x12)/12<BR>\n" );
document.write( "hence sum of numbers =7*12=84=(x1+x2+....+x11+x12)<BR>\n" );
document.write( "median is 6..that is the middle term is 6..but total number of terms is 12 so there would be 2 middle terms...namely x6 and x7...by convention in such cases their average is taken as median..so (x6+x7)/2=6...or....x6+x7=2*6=12.<BR>\n" );
document.write( "mode is 8 ...that is the frequency of occurence of mode or number 8 should be maximum...<BR>\n" );
document.write( "now there are no unique answers for this... we are just to give any set of 12 numbers satisfying the above 3 conditions.<BR>\n" );
document.write( "say one set of numbers could be then ....<BR>\n" );
document.write( "   let us put median as 6 ..by taking both x6 and x7 as 6 each...<BR>\n" );
document.write( "now 8 should occur maximm numer of times ...so let x8=x9=x10=x11=8..here 8 occurs 4 times.<BR>\n" );
document.write( "let us take x12=16 say...<BR>\n" );
document.write( "total of numbers we have taken so far is 6+6+8*4+16=60<BR>\n" );
document.write( "now take x1 to x5 so that thy add up to  84-60=24...since total should be 84 to get mean 7 as given above...we only have to see that no number should occur more than 4 times as mod of 8 ,we took with frequency of 4 which should be the highest...<BR>\n" );
document.write( "so let us take x1=4,x2=4,x3=5,x4=5,x5=6..which satisfies all the above conditions<BR>\n" );
document.write( "so the set of numbers in increasing order are 4,4,5,5,6,6,6,8,8,8,8,16....<BR>\n" );
document.write( "their mean is (4+4+5+5+6+6+6+8+8+8+8+16)/12=84/12=7<BR>\n" );
document.write( "median is 6 ,since middle most number /numers are 6.<BR>\n" );
document.write( "mode is 8 as 8 occurs 4 times ,the maximum frequency.. </SPAN>\n" );
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