Question 1104153
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There are 8 numbers, so the median is the average of the 4th and 5th.<br>
The sum of the 8 numbers is 3x+27; if the mean is 7, then the sum is 56.  So
{{{3x+27=56}}}
{{{3x=29}}}
{{{x=29/3}}}
So the 6 numbers given are
2 3 3 4 6 9
and the two numbers we calculated are 9 2/3 and 19 1/3.<br>
We know those numbers satisfy the condition that the mean is 7, because we used that fact to find the two numbers that were not given.<br>
And the median of the set of all 8 numbers is 5, because the middle two are 4 and 6.<br>
So the value of x that gives the data set a mean of 7 and a median of 5 is 29/3, or 9 2/3.