Respuesta :
Answer:
18
Step-by-step 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 [tex]x[/tex]
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, [tex]x[/tex]
For odd number of observation:
[tex]Median=\frac{n+1}{2}=\frac{5+1}{2} =\frac{6}{2} =3[/tex]
That means 3rd term is the median:-
Median = 14
Mean = Median = 14 ( given )
As we know:
[tex]Mean=\frac{Sum\ of\ observations}{Number\ of\ observations}[/tex]
[tex]14 = \frac{14+8+16+14+x}{5} \\ \\ 14=\frac{52+x}{5} \\ \\ By\ cross\ multiplication\\ \\ 52+x=14\times5\\ \\ 52+x=70\\ \\ Subtracting\ both\ sides\ by\ 52\\ \\ 52-52+x=70-52\\ \\ x=18[/tex]
Thus, the 5th number is 18 that Ms. Hernandez was thinking of.
