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. The new observation is:

19.8

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9.8

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9.2

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8.8

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Solution

The correct option is D
8.8

Given: Mean of 20 observations = 19.3
$\Rightarrow \frac{S u m o f a l l o b s e r v a t i o n s}{20} = 19.3$
$\Rightarrow S u m o f a l l o b s e r v a t i o n s = 19.3 \times 20$
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: $\frac{S u m o f a l l o b s e r v a t i o n s + x}{21} = (19.3 - 0.5) = 18.8$
$\Rightarrow s u m o f a l l o b s e r v a t i o n s + x = 18.8 \times 21$
$\Rightarrow x = 18.8 \times 21 - S u m o f a l l o b s e r v a t i o n s$
$\Rightarrow x = (18.8 \times 21) - (19.3 \times 20)$
$\Rightarrow x = 394.8 - 386$
$\Rightarrow x = 8.8$

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