Question

The mean of $27$ observations of a variable is $18$. Three more observations are made and the values of these observations are $16,18$ and $50$. What is the mean of these $30$ observations?

• A. $18$
• B. $19$
• C. $25.5$
• D. Cannot be determined due to insufficient data

Answer 1

The correct option is B $19$

Given that mean of $27$ observations are $18.$

Therefore,

$18=\frac{\text{sum of the 27 observations}}{27}$

$\Rightarrow \text{sum of the 27 observations}=27\times 18$

$=486\dots \left(i\right)$

Given that three more observations $16,18,50$ are added.

Therefore,

$\text{mean}=\frac{\text{sum of the 27 observations}+16+18+50}{30}$

$\Rightarrow \text{mean}=\frac{\text{sum of the 27 observations}+84}{30}$

$\Rightarrow \text{mean}=\frac{486+84}{30}$ (from $\left(i\right)$)

$\Rightarrow \text{mean}=\frac{570}{30}$

$\Rightarrow \text{mean}=19$