The average of 25 numbers is 54. The average of the first 13 numbers and that of the last 13 numbers are 52.8 and 62.2, respectively. If the 13th number is excluded, then what is the average of the remaining numbers (correct to one decimal place)?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 50.2.
Total of 25 numbers = 25 × 54 = 1350
Sum of first 13 numbers = 13 × 52.8 = 686.4
Sum of last 13 numbers = 13 × 62.2 = 808.6
13th number counted twice:
Total = 686.4 + 808.6 − x = 1350
⇒ x = 145 (13th number)
New sum = 1350 − 145 = 1205
New average = = 50.2