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

Question

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 thefirst 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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