SOLUTION: If the mean, median, and mode are all equal for the set {10, 50, 60, 80, x} what can you say about the value of x?

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Question 957295: If the mean, median, and mode are all equal for the set {10, 50, 60, 80, x} what can you say about the value of x?
Answer by erica65404(394) About Me  (Show Source):
You can put this solution on YOUR website!
This is a guess and check problem.

%2810%2B50%2B60%2B80%2Bx%29%2F5 or %28200%2Bx%29%2F5 is an equation that will represent the mean of this set of numbers (add all the numbers up and divide by the amount of numbers you have).

Since the mean median and mode are the same we know that x will be one of the current numbers so that a mode is present.

I chose 80 for x to start with.
When I plugged 80 into this equation the mean is 56.

{10, 50, 60, 80, 80}

Now I look at the set and see that if x was 80, the median would be 60.
A median of 60 is too high.
x=80 is incorrect


So now I choose 60 for x.
The mean is now 52.

{10, 50, 60, 60, 80}

Look at the set and the median is 60.
60 is still too high of a median.

Now we choose 50 for x.
The mean is 50.

{10, 50, 50, 60, 80}

The median is 50.


The mode median and mean are the same number now so x = 50.