The mean of 15 observations is 8. If the mean of the first eight observations is 7 and that of the last eight observations is 10, then the value of the 8th observation is _____.

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Solution

The correct option is A
16

We know that,
Mean = $\frac{S u m o f a l l o b s e r v a t i o n s}{N u m b e r o f o b s e r v a t i o n s}$

Sum of values of all the observations
$= M e a n \times N u m b e r o f o b s e r v a t i o n$
$= 15 \times 8$
$= 120$

So, sum of the first eight observations
$= M e a n \times N u m b e r o f o b s e r v a t i o n$
$= 7 \times 8$
$= 56$
Sum of the last eight observations
$= M e a n \times N u m b e r o f o b s e r v a t i o n$
$= 10 \times 8$
$= 80$

Hence, value of the $8^{t h}$ observation
$= (80 + 56) - 120$
$= 16$

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