Akash calculated his average over the last 18 tests and found it to be 76. He…
2026
Akash calculated his average over the last 18 tests and found it to be 76. He finds out that the marks for three tests have been inverted by mistake. The correct marks for these tests are 56, 67 and 97. What is the percentage difference between his actual average and his incorrect average?
- A.
1.33
- B.
1.73
- C.
1.66
- D.
No difference
Attempted by 10 students.
Show answer & explanation
Correct answer: D
Concept: The average of a set of values equals the total sum divided by the number of values. If some entries in the data are later corrected, the average changes only if the total sum changes; if the net change in the sum is zero, the average -- and hence the percentage difference between the old and new averages -- stays at 0%.
The three tests were entered with their marks digit-reversed: 65 should be 56, 76 should be 67, and 79 should be 97.
Find the change in each test's mark (correct minus incorrect): 56 − 65 = −9, 67 − 76 = −9, and 97 − 79 = +18.
Add the three changes to get the net change in the total sum of all 18 marks: −9 + (−9) + 18 = 0.
Since the net change in the sum is 0, the sum of all 18 marks -- and therefore the average (sum ÷ 18) -- stays exactly the same before and after the correction.
Percentage difference = (corrected average − incorrect average) ÷ incorrect average × 100 = 0 ÷ 76 × 100 = 0%.
Cross-check: Add the three correct marks and the three incorrect marks separately -- 56 + 67 + 97 = 220, and 65 + 76 + 79 = 220. The two totals are equal, confirming the sum of all 18 marks does not change, regardless of the stated average (76) or the number of tests (18).
So Akash's actual average is exactly the same as his incorrect average -- there is no difference.