document.write( "Question 20536: 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
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Algebra.Com's Answer #9893 by AnlytcPhil(1807) $\"\"$ $\"About$

You can put this solution on YOUR website!

I suggest starting with all 7's, so the mean will be 7
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document.write( "7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7
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document.write( "We can add anything to any of these numbers and as long as we subtract the same
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document.write( "away as the total amount we add on, the mean will remain 7, for the sum will
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document.write( "remain the same.  But let's agree to do it so that the 12 numbers will remain
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document.write( "in ascending order from small to large.
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document.write( "To make the median 6, we must make the middle two numbers have a mean of 6.
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document.write( "The easiest way is to make them both 6.  But to do this and keep ascending
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document.write( "order we'll have to subtract 1 from each of the first seven 7's. So we'll need
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document.write( "to add 7 among the last 5 7's, trying to make as many 8's as possible since the
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document.write( "mode must be 8.  The most number of 8's we can make is four, by adding 1 to
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document.write( "each of the 7's on the right except the last one, to which we must add  3. 
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document.write( "6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 10
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document.write( "But there are only four 8's, and seven 6's, so we must reduce the number of 6's
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document.write( "below four. So we subtract 1 from each of the first four 6's, and add 4 to the
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document.write( "10 on the far right, giving
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document.write( "5, 5, 5, 5, 6, 6, 6, 8, 8, 8, 8, 14
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document.write( "But this makes four 5's, causing a tie between the 5's and the 8's for being
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document.write( "the mode, so we subtract 1 from the first 5 and add one to the 14 on the far
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document.write( "right, giving
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document.write( "4, 5, 5, 5, 6, 6, 6, 8, 8, 8, 8, 15
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document.write( "That's one answer.  There are lots of other possible answers, such as  
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document.write( "2, 4, 4, 5, 5, 5, 7, 8, 8, 8, 8, 20
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document.write( "Edwin
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document.write( "AnlytcPhil@aol.com  \n" );
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