Question

The mean of 15 observations is 8. If the mean of the values of first eight observations is 7 and that of the values of last eight observations is 10,

then the value of the 8th observation is :

• A. 12
• B. 16

Answer 1

The correct option is B

16

Sum of values of all the observations = 15 x 8 = 120.

Similarly we can obtain sum of the values of first eight and last eight observations.

So, sum of values of first eight observations = 56 and sum of the values of last eight observations = 80.

The value of $8^{th}$ observation is equal to the half the difference between the sum the values of first eight and last eight observations respectively and sum of all the values of the observations.

Hence, we get value of $8^{th}$observation
$=\frac{(80+56)-120}{2}=\frac{16}{2}=8$

It should be noted that the value of the $8^{th}$ observation is included both in 80 and 56.

Hence, after finding the difference between 136 and 120, we get twice the value of the 8th observation.