The average of 25 numbers is 64. The averages of the first 13 numbers and that of the last 13 numbers are 62.8 and 72.2, respectively. If the 12th number is 61, and if the 12th and 13th numbers are excluded, then what is the average of the remaning numbers (correct to one decimal place)?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 60.2.
Average = Sum of observation × no of observation
Sum of 25 numbers = 25 × 64 = 1600
Sum of first 13 number = 13 × 62.8 = 816.4
Sum of last 13 number = 13 × 72.2 = 938.6
13 number = 816.4 + 938.6 - 1500 = 155
If 12 and 13 number is removed then sum of the remaining 23 numbers = 1600 - 61 - 155 = 1384
Required average = 1384/23 = 60.2.