# Given the set:  {1,13,-7,8,x,-2,-9,2} , for what x would the mean of the set be 0?

Dec 28, 2015

$x = - 6$

#### 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)

$\textcolor{w h i t e}{\times} 0 = \frac{1}{8} {\sum}_{i = 1}^{8} {a}_{i}$
$\implies \frac{x - 9 - 7 - 2 + 1 + 2 + 8 + 13}{8} = 0$

Multiply both sides by $\textcolor{red}{8}$
$\textcolor{w h i t e}{\times} \textcolor{red}{8 \times} \frac{x - 9 - 7 - 2 + 1 + 2 + 8 + 13}{8} = \textcolor{red}{8 \times} \left(0\right)$
$\implies x + 6 = 0$

Add $\textcolor{red}{- 6}$ to both sides
$\textcolor{w h i t e}{\times} x + 6 \textcolor{red}{- 6} = 0 \textcolor{red}{- 6}$
$\implies x = - 6$