Correct option is D
Given:
Total numbers = 41
Average of all 41 numbers = 33
Average of the first 17 numbers = 41
Average of the last 25 numbers = 27
The 17th number is excluded.
Formula Used:
Sum of observations = Average × Number of observations
Sum of remaining numbers = Total sum - 17th number
Solution:
Total sum of 41 numbers:
Total sum = 33 × 41 = 1353
Sum of the first 17 numbers:
Sum of first 17 = 41 × 17 = 697
Sum of the last 25 numbers:
Sum of last 25 = 27 × 25 = 675
The 17th number is common to both the first 17 and last 25 numbers.
Let the 17th number be x
Total sum = Sum of first 17 + Sum of last 25 - x
1353 = 697 + 675 - x
1353 = 1372 - x
x = 1372 - 1353
x = 19
Sum of the remaining numbers after excluding the 17th number:
Sum of remaining numbers = 1353 - 19 = 1334
Number of remaining numbers = 40
New Average = = 33.35
Thus, The average of the remaining numbers is 33.35
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