Mean is calculated by adding all numbers and dividing by how many there are. I have set up an equation to find x from the given mean.
[tex] \frac{12.5 -10 -7.5 + x}{4} = 11.5 [/tex]
To cancel out the denominator, multiply both sides by 4.
[tex] 4(\frac{12.5 -10 -7.5 + x}{4}) = 4(11.5) [/tex]
When that is done, you are left with:
[tex] 12.5 -10 -7.5 + x = 46 [/tex]
Combine like terms:
[tex] -5 + x = 46 [/tex]
Add 5 to both sides, cancelling out the -5 on the left.
[tex] x = 51 [/tex]
Your answer is 51.
If you want to check your work, plug in 51 for x.
[tex] \frac{12.5 - 10 - 7.5 + 51}{4} = 11.5 [/tex]
[tex] \frac{46}{4} = 11.5 [/tex]
So remember that the mean is [tex] \frac{\textsf{sum of all numbers in the data set}}{\textsf{how many numbers there are in the data set}} [/tex] . In our case, the equation is [tex] \frac{12.5+(-10)+(-7.5)+x}{4}=11.5 [/tex]
Firstly, add up everything in the numerator: [tex] \frac{-5+x}{4}=11.5 [/tex]
Next, multiply both sides by 4: [tex] -5+x=46 [/tex]
Lastly, add both sides by 5 and your answer will be [tex] x=51 [/tex]
