The twelve numbers 3,6,9,12,4,6,8,10,12,14,x,y have a mode of 6 and a mean of 8. Find the values of x and y and the median of the above twelve numbers.

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The number 3,6,9,12,4,6,8,10,12,14 have a sum of 84.  If 12 numbers have an mean if 8, they have to have a sum of 96.  So, the final 2 numbers have to total 12.  Since the mode has to be 6 with these numbers, and right now the numbers are bi-modal with 6 and 12, then one of these numbers has to be 6.  Given that and their sum as to be 12, both numbers have to be 6.  So, we would have:

3,6,6, 6, 9,12,4,6,8,10,12,14

For the 12 numbers.

For the median, we are looking for the middle of the 12 numbers.  First, we have to put them in numerical order:

3, 4, 6, 6, 6, 6, 8, 9, 10, 12, 12, 14

The median is the middle value of these numbers.  However, if you consider, there isn't one single "middle value".  6 and 8 are the middle values.  In this case, we take the average of the middle values:

(6+8)/2 = 7

So, 7 is the median value for these numbers.

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