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?
2 Answers
justaguide | College Teacher | (Level 2) Distinguished Educator
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
hala718 | High School Teacher | (Level 1) Educator Emeritus
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.