Question

The mean of 10 observations is 15.3. If two observations 6 and 9 are replaced by 8 and 14 respectively. Find the new mean.

Answer 1

The mean of 10 observations = 15.3
Then sum of the 10 observations = 10 × 15.3 = 153
If observation 6 and 9 are replaced by 8 and 14 respectively,
then the new sum of 10 observations = 153 - (6+9) + 8 + 14
= 153 - 15 + 22
= 175 - 15
= 160
So, the new mean of the 10 observations = 160/10
= 16  Answer

Answer 2

Due to the replacement,  the increase in the total of the observations will be equal to       (8 - 6) + (14 - 9) = 7

The increase in the average (mean)
   = increase in the total / number of observations
   = 7 / 10 = 0.7

Thus the new mean is = 15.3 + 0.7 = 16.