Question

The mean of a set of 20 observations is 19.3. The mean is reduced by 0.5 when a new observation is added to the set. What is the new observation that has been added?

• A. 19.8
• B. 9.8
• C. 9.2
• D. 8.8

Answer 1

The correct option is D

8.8

Given: Mean of 20 observations = 19.3
$\Rightarrow \frac{\text{sum of all observation}}{20}=19.3$
$\Rightarrow$ sum of all observation = 19.3 $\times$ 20
Now, if a new observation is added, then the mean is reduced by 0.5.
Let the new observation added be $x$.
So the new mean becomes: $\frac{\text{sum of all observation}+x}{21}=(19.3-0.5)=18.8$
$\Rightarrow$ sum of all observation + x = 18.8 $\times$ 21
$\Rightarrow x=18.8\times 21$ - sum of all observation
$\Rightarrow x=(18.8\times 21)-(19.3\times 20)$
$\Rightarrow x=394.8-386$
$\Rightarrow x=8.8$.