Question

Ms. Hernandez began her math class by saying: I’m thinking of 5 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? What is the 5th number Ms. Hernandez is thinking of?

Answer 1

18

Explanation:

Given:

Ms. Hernandez began her math class by saying: I’m thinking of 5 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?

What is the 5th number Ms. Hernandez is thinking of?

Solution:

Let 5th number is
`x`

First of all we will calculate median for the following data:

14, 8, 16, and 14

Arrange it into ascending order:-

8, 14, 14, 16,
`x`

For odd number of observation:

`Median=(n+1)/(2)=(5+1)/(2) =(6)/(2) =3`

That means 3rd term is the median:-

Median = 14

Mean = Median = 14 ( given )

As we know:

`Mean=(Sum\ of\ observations)/(Number\ of\ observations)`

`14 = (14+8+16+14+x)/(5) \\ \\ 14=(52+x)/(5) \\ \\ By\ cross\ multiplication\\ \\ 52+x=14*5\\ \\ 52+x=70\\ \\ Subtracting\ both\ sides\ by\ 52\\ \\ 52-52+x=70-52\\ \\ x=18`

Thus, the 5th number is 18 that Ms. Hernandez was thinking of.