Question

The algebraic sum of the deviations of $20$ observations measured from $30$ is $2$. What would be the mean of the observations?

• A. $30$
• B. $32$
• C. $30.2$
• D. $30.1$

Answer 1

Answer: (D)

$30.1$

Let the $20$ deviations be $a_1,a_2,...,a_{20}$

Therefore the observations are $(30+a_1),(30+a_2),...,(30+a_{20})$

Given that sum of the deviations is $2$

Therefore, $a_1+a_2+...+a_{20}=2$ ------(1)

Hence, $mean=\frac{(30+a_1)+(30+a_2)+...+(30+a_{20})}{20}$

$⟹mean=\frac{a_1+a_2+...+a_{20}+20\left(30\right)}{20}$

$⟹mean=\frac{2+20\left(30\right)}{20}$ (from (1))

$⟹mean=\frac{602}{20}=30.1$