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 8^th observation is ___ .

Answer 1

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 of first 8 observations = 8×7 = 56……(1)

Mean of last 8 is10.

i.e. sum of last 8 observations = 10×8 = 80……(2)

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

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

8th term = 136 -120 = 16