The average of 21 numbers is 66. The average of the first 9 numbers is 63.7 and that of the last 13 numbers is 69.9. If the 9th number is excluded, then what is the average of the remaining numbers?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 64.5.
Average of 21 numbers = 66
Average of first 9 numbers = 63.7
Average of last 13 numbers = 69.9
Total sum = 21 × 66 = 1,386
Sum of first 9 numbers = 9 × 63.7 =573.3
Sum of last 13 numbers = 13 × 69.9 = 908.7
Sum of first 9 numbers + Sum of last 13 numbers = 573.3 + 908.7 = 1,482
The actual total of all 21 numbers is only 1,386:
Overcounted amount = 1,482 − 1,386 = 96
The 9th number is 96.
Sum of remaining 20 numbers = 1,386 − 96 = 1,290
Average =