Given a set  {-15,1,200,x,1} , for what x would the mean of the set be -15?

Dec 11, 2015

$\textcolor{w h i t e}{\times} - 262$

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)

$\textcolor{w h i t e}{\times} - 15 = \frac{1}{5} {\sum}_{i = 1}^{5} {a}_{i}$
$\implies \frac{- 15 + 1 + 200 + x + 1}{5} = - 15$

Multiply both sides by $5$
$\textcolor{w h i t e}{\times} \textcolor{red}{5 \cdot} \frac{- 15 + 1 + 200 + x + 1}{5} = \textcolor{red}{5 \cdot} \left(- 15\right)$
$\implies x + 187 = - 75$

Add $- 187$ to both sides
$\textcolor{w h i t e}{\times} x + 187 \textcolor{red}{- 187} = - 75 \textcolor{red}{- 187}$
$\implies x = - 262$