# Five numbers such that their mean is equal to their median. If 4 of the numbers are 14, 8, 16, and 14, what is the 5th number?

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Given the set of numbers 14 , 8, 16, 14 , and x

We know that the mean = the median.

Let us arrange the numbers from smallest to largest.

==> 8, 14, 14, 16, x

Since we so not know that value of x we will try and determine the median.

If x is 14 , then the median is 14

If x is between 8 and 14 ==> the median also 14

If x is between 14 and 16 ==> the median is 14

If x is less than 8 ==> the median is 14

If x is larger than 16 , the median is 14.

Then, we conclude that no matter what is the values of x, the median is 14.

Now we will calculate the mean.

==> The mean = (8+14+14+16+x) / 5 = The median = 14

==> (52 + x)/5 = 14

We will multiply by 5.

==> 52 + x = 70

==> x = 70 - 52 = 18

**Then, the fifth number is 18.**

The numbers we have are 14 , 8, 16 and 14. Let us take the 5th number as X.

Now the mean of the numbers is equal to the median.

So (14 + 8 + 16 + 14 + X)/5 = 14

=> (52 + X)/5 = 14

=> 52 + X = 70

=> X = 70 - 52

=> X = 18

**The fifth number is 18**