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 find the value of the 8^th observation.

• A. 15
• B. 16
• C. 17
• D. 18

Answer 1

The correct option is B

16

Given mean of 15 observation =8

Mean=$\frac{Totalsumofobservation}{totalnumberofobservations}$

This means sum total =15×8=120

Mean of first 8 is 7

i.e. sum total =8×7=56……(1)

Mean of last 8 is10

i.e. sum total=10×8=80……(2)

So the sum of equation 1&2 is 56+80=136

But since we added the $8^{th}$ term twice

so 136-120=16

i.e. the $8^{th}$ term