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

Dec 28, 2015

$x = 22$

#### 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)

$\textcolor{w h i t e}{\times} 3 = \frac{1}{7} {\sum}_{i = 1}^{7} {a}_{i}$
$\implies \frac{x - 4 - 3 + 1 + 1 + 2 + 2}{7} = 3$

Multiply both sides by $\textcolor{red}{7}$
$\textcolor{w h i t e}{\times} \textcolor{red}{7 \times} \frac{x - 4 - 3 + 1 + 1 + 2 + 2}{7} = \textcolor{red}{7 \times} 3$
$\implies x + 31 = 21$

Add $\textcolor{red}{+ 1}$ to both sides
$\textcolor{w h i t e}{\times} x - 1 \textcolor{red}{+ 1} = 21 \textcolor{red}{+ 1}$
$\implies x = 22$