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?

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) (Show Source): You can put this solution on YOUR website!
This is a guess and check problem.

or 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.

RELATED QUESTIONS
The following question has to do with mean, median, and mode: Which statement is... (answered by solver91311)

Explain what is meant by mean, median, mode, variance, and standard deviation for a set... (answered by stanbon)

Which of the following statements is true regarding the normal distribution? a.... (answered by user_dude2008)

What is the mean, median and mode of the following distribution? Ages Number 40 (answered by solver91311)

Suppose you calculated the mean, median, mode, and sample standard deviation of a data... (answered by ikleyn)

A set of 7 positive integers has a median 3 and unique mode 4. If you add two 2's to... (answered by Edwin McCravy)

In January of 2017, you planted a rare variety of tomato. In 2 month time, you recorded... (answered by CPhill)

Please help me solve this problem: In an exercise gym, 5 different people used a... (answered by jim_thompson5910)