Question

The average of 15 observations is 29. if the average of first 8 observations is 27 and that of last 8 observations is 31. the what will be the 8th observation? 
1. 27
2. 31
3. 30
4. 29

Answer 1

Correct Answer - Option 4 : 29

GIVEN:

average of 15 observations = 29 

average of first 8 = 27 

average of last 8 = 31

FORMULA USED:

average = sum of all observations/total number of observations

CALCULATION:

sum of 15 observations = 15 × 29 = 435

sum of first 8 observations = 8 × 27 = 216

sum of last 8 observations = 8 × 31 = 248

the 8th observation is repeated twice in sum of first and last observations

8th observation = (sum of first 8) + (sum of last 8) - (sum of 15 observations) 

⇒ 216 + 248 - 435 = 29

∴ 8th observation is 29