Question

Find the value of x. 12.5, -10, -7.5, x. the mean is 11.5

Answer 1

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.

$\frac{12.5 -10 -7.5 + x}{4} = 11.5$

To cancel out the denominator, multiply both sides by 4.

$4(\frac{12.5 -10 -7.5 + x}{4}) = 4(11.5)$

When that is done, you are left with:

$12.5 -10 -7.5 + x = 46$

Combine like terms:

$-5 + x = 46$

Add 5 to both sides, cancelling out the -5 on the left.

$x = 51$

Your answer is 51.

If you want to check your work, plug in 51 for x.

$\frac{12.5 - 10 - 7.5 + 51}{4} = 11.5$

$\frac{46}{4} = 11.5$

Answer 2

So remember that the mean is $\frac{\textsf{sum of all numbers in the data set}}{\textsf{how many numbers there are in the data set}}$ . In our case, the equation is $\frac{12.5+(-10)+(-7.5)+x}{4}=11.5$

Firstly, add up everything in the numerator: $\frac{-5+x}{4}=11.5$

Next, multiply both sides by 4: $-5+x=46$

Lastly, add both sides by 5 and your answer will be $x=51$