# Given a set  {-2,x,-3,-4,1,15,22,2} , for what x would the mean of the set be -12?

##### 1 Answer
Dec 28, 2015

$x = - 127$

#### Explanation:

$\textcolor{w h i t e}{\times} \overline{a} = \frac{1}{n} {\sum}_{i = 1}^{n} {a}_{i}$ (the mean of a set of n data points)

$\textcolor{w h i t e}{\times} - 12 = \frac{1}{8} {\sum}_{i = 1}^{8} {a}_{i}$
$\implies \frac{x - 4 - 3 - 2 + 1 + 2 + 15 + 22}{8} = - 12$

Multiply both sides by $\textcolor{red}{8}$
$\textcolor{w h i t e}{\times} \textcolor{red}{8 \times} \frac{x - 4 - 3 - 2 + 1 + 2 + 15 + 22}{8} = \textcolor{red}{8 \times} - 12$
$\implies x + 31 = - 96$

Add $\textcolor{red}{- 31}$ to both sides
$\textcolor{w h i t e}{\times} x + 31 \textcolor{red}{- 31} = - 96 \textcolor{red}{- 31}$
$\implies x = - 127$