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If the average of 9 numbers is 17 and one number is removed, the average of the remaining 8 numbers becomes 15. What is the value of the removed number?
39
33
37
35
33
Calculate the difference in sum: (9 × 17) - (8 × 15) = 153 - 120 = 33. Alternatively, think: The removed number takes away its own value (17) plus the 'surplus' it was providing to the other 8 numbers (8 numbers × 2 drop in average) = 17 + 16 = 33.
Initial set of 9 numbers has an average of 17. After removing one number, the new set of 8 numbers has an average of 15.
Sum=Average×Count
Calculate the difference in sum: (9 × 17) - (8 × 15) = 153 - 120 = 33. Alternatively, think: The removed number takes away its own value (17) plus the 'surplus' it was providing to the other 8 numbers (8 numbers × 2 drop in average) = 17 + 16 = 33.
Many students calculate 17 - 15 = 2 and multiply by 9, or forget that the count of numbers changes from 9 to 8, leading to errors in the total sum calculation.
Calculate initial total sum
To find the sum of all 9 numbers, multiply the average by the count of numbers.
Sum9=9×17=153
Calculate final total sum
After one number is removed, 8 numbers remain. Multiply the new average by the new count.
Sum8=8×15=120
Determine the removed number
The difference between the initial sum and the final sum is the value of the removed number.
Removed=153−120=33
B is correct because the difference between the total sum of 9 numbers (153) and the total sum of 8 numbers (120) is 33.
This concept is fundamental for Data Interpretation questions where you need to calculate a missing observation in a trend or dataset analysis.
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