Question

The average of six numbers is -3-65. If five of the numbers are each -3.2, what is the sixth number?

Answer 1

`\bar{x}=(\sum ^(\infty)_(n\mathop=0)xi)/(n)`

The definition of average allows us to find the missing value.

the information given is

`\begin{gathered} \bar{x}=-3.65 \\ x_1=-3.2 \\ x_2=-3.2 \\ x_3=-3.2 \\ x_4=-3.2 \\ x_5=-3.2 \\ x_6=\text{?} \\ n=6 \end{gathered}`

replace in the formula knowin that all the -3.2 can be written as 5*(-3.2)

`-3.65=(5\cdot(-3.2)+x_6)/(6)`

solve for x6

`\begin{gathered} -3.65\cdot6=(5\cdot-3.2)+x_6 \\ -21.9=-16+x_6 \\ -21.9+16=x_6 \\ x_6=-5.9 \end{gathered}`

Chech if answer is correct

`\begin{gathered} -3.65=(5\cdot(-3.2)-5.9)/(6) \\ -3.65=-3.65 \end{gathered}`

answer= the sixth number is -5.9