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?

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.