A student needed to find the arithmetic mean of the numbers 3, 11, 7, 9, 15, 13, 8, 19, 17, 21, 14 and x. He found the mean to be 12. What is the value of x?
12
5
7
9
Explanation:
$\dfrac{\text{3+11+7+9+15+13+8+19+17+21+14+}x}{12}$ $ = 12$
$\Rightarrow \dfrac{137 + x}{12} = 12\\~\\$
$\Rightarrow 137 + x = 144\\~\\$
$\Rightarrow x = 144 - 137 = 7$