Question

The mean of $10$ observations is $5$. If $2$ is added to each observation and then multiplied by $3$, then what will be the new mean?

• A. $5$
• B. $7$
• C. $15$
• D. $21$

Answer 1

The correct option is D $21$

Let the observations be $a_1,a_2,...,a_{10}$

Given that, mean of the observations is $5$

Therefore, $5=\frac{a_1+a_2+...a_{10}}{10}$

$⟹a_1+a_2+...a_{10}=50$ -----(1)

Given that, $2$ is added to each observation and multiplied by 3

Therefore, $\text{new mean}=\frac{(a_1+2)3+(a_2+2)3+...(a_{10}+2)3}{10}$

$⟹\text{new mean}=\frac{(a_1+a_2+...+a_{10})3+(10\times 2)3}{10}$

$⟹\text{new mean}=\frac{\left(50\right)3+\left(20\right)3}{10}$

$⟹\text{new mean}=\frac{210}{10}=21$