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