document.write( "Question 1104153: What is the value of x if the numbers x, 2x, 3, 6, 4,3,2,9 have a mean of 7 and median 5? \n" ); document.write( "

Algebra.Com's Answer #718895 by greenestamps(13206) $\"\"$ $\"About$

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\n" ); document.write( "There are 8 numbers, so the median is the average of the 4th and 5th.

\n" ); document.write( "The sum of the 8 numbers is 3x+27; if the mean is 7, then the sum is 56. So
\n" ); document.write( " $\"3x%2B27=56\"$
\n" ); document.write( " $\"3x=29\"$
\n" ); document.write( " $\"x=29%2F3\"$
\n" ); document.write( "So the 6 numbers given are
\n" ); document.write( "2 3 3 4 6 9
\n" ); document.write( "and the two numbers we calculated are 9 2/3 and 19 1/3.

\n" ); document.write( "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.

\n" ); document.write( "And the median of the set of all 8 numbers is 5, because the middle two are 4 and 6.

\n" ); document.write( "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. \n" ); document.write( "

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