Question : The average of 16 numbers is 35. It was found later that four numbers 18, 17, 24, and 35 were taken by mistake. What is the new average after removing these numbers?
Option 1: 38.83
Option 2: 42.33
Option 3: 46.66
Option 4: 33.33
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Correct Answer: 38.83
Solution :
Given that the average of 16 numbers is 35, we can calculate the sum of those 16 numbers as follows:
Sum = Average × Count
⇒ Sum = 35 × 16 = 560
So, Adjusted Sum = Sum – Sum of Mistaken Numbers
⇒ Adjusted Sum = 560 – (18 + 17 + 24 + 35) = 466
Since we removed four numbers, the count of the remaining numbers is 16 – 4 = 12.
The new average is then calculated by dividing the adjusted sum by the new count,
New average =$\frac{\text{ Adjusted Sum}}{\text{New Count}} = \frac{466}{12}$ = 38.83 (rounded to two decimal places)
Hence, the correct answer is 38.83.
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