### If the mean of $6$ observations $x, x + 2, x + 4, x + 6, x + 8, x + 10$ is $10$, find the value of $x.$

$5$
1. We know, $$\text { Mean } = \dfrac {\text{Sum of observations}} {\text{Number of observations}}$$
2. Thus, mean of the given observations $$= \dfrac { x + x + 2+ x + 4+ x + 6+ x + 8+ x + 10 } { 6 } = \dfrac { 6 x + 30 } { 6 }$$ But we are given that the mean is $10.$ \begin{aligned} \therefore \space & \dfrac { 6 x + 30 } { 6 } = 10 \\ \implies & 6 x + 30 = 60 \\ \implies & 6 x = 30 \\ \implies & x = 5 \end{aligned}
3. Hence, the value of $x$ is $5$.