The mean of 15 observations is 8. If the mean of the first eight observations

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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 _____.

Options:

A . 16

B . 15

C . 14

D . 13

Answer: Option A
:
A

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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