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 _____.

• A. 16
• B. 15
• C. 14
• D. 13

Answer 1

The correct option is A

16

We know that,
Mean = $\frac{Sumofallobservations}{Numberofobservations}$

Sum of values of all the observations
$=Mean\times Numberofobservation$
$=15\times 8$
$=120$

So, sum of the first eight observations
$=Mean\times Numberofobservation$
$=7\times 8$
$=56$
Sum of the last eight observations
$=Mean\times Numberofobservation$
$=10\times 8$
$=80$

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