SOLUTION: Starting with the data values 70 and 100, add three data values to the sample so that the mean is 74, the median is 85, and the mode is 85. Please show all of your work.

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Question 481639: Starting with the data values 70 and 100, add three data values to the sample so that the mean is 74, the median is 85, and the mode is 85. Please show all of your work.
Found 2 solutions by Edwin McCravy, MathTherapy:
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
Sorry, I misread the problem the first time. It's corrected now 
The median of a odd number of numbers is right in the middle. So
we just have two blanks to fill in

__, 70, 85, __, 100

If these numbers are from smallest to largest, then to make 85 the
mode we have to put in another 85, so there will be more 85's than
anything else.  So now we have:

__, 70, 85, 85, 100

Since the mean must be 74, the sum of all 5 numbers has to 
be 5×74 or 370.  The ones we already have add up to 

70+85+85+100 = 340

so we have to put 30 in the blank on the far left.  So the answer
is

30, 70, 85, 85, 100

Edwin
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
We start with 70 and 100

Mode is 85, so we need at least 2 85s.
70, 85, 85, 100

Median is 85, so we’re on the right track
By letting N equal 5th number, and since mean is 74, then

340 + N = 370
N = 370 – 340 = 30
Therefore, the 5 numbers are 30, 70, 85, 85, and 100.

As seen, the median is 85, and the mode is also 85, and the mean is (370/5).
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