SOLUTION: what number should be added to the following set of data so that the mean,median,and mode will become the same number ? 91,93,93,95,95,98,100

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Question 174453: what number should be added to the following set of data so that the mean,median,and mode will become the same number ?
91,93,93,95,95,98,100
Found 2 solutions by checkley77, Edwin McCravy:
Answer by checkley77(12844)   (Show Source): You can put this solution on YOUR website!
91,93,93,(95),95,95,98,100
Proof:
Sum=760
760/8=95 median, mode, mean.
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
what number should be added to the following set of data so that the mean,median,and mode will become the same number ?
91,93,93,95,95,98,100

Since there are two 93's and two 95's, it order to have 
a mode (the number that occurs the most number of times),
the number to add must either be a 93 or a 95.  The 95
is right in the middle, and the 93 is more toward the 
bottoms, so 95 seems the most promising, so I'll add it
in the middle and check to see if it works:

91,93,93,95,95,95,98,100

91+93+93+95+95+95+98+100=760

760÷8 = 95, the mean.

The middle two numbers are both 95, so 95 is the median.

There are three 95's so there are more of them than
any other number, so 95 is the mode, too.

Edwin
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