In an examination, the mean of the marks scored by a class of 30 students was…
2018
In an examination, the mean of the marks scored by a class of 30 students was calculated as 58.5. Later, it was found that one student’s mark had been copied as 57 instead of 75. Find the correct mean.
- A.
51.9
- B.
59.1
- C.
20.9
- D.
28.9
Attempted by 1 students.
Show answer & explanation
Correct answer: B
Concept
The arithmetic mean equals the sum of all observations divided by the number of observations.
If one recorded value is replaced by its correct value, adjust the total by the difference and divide by the unchanged number of observations.
Application
The incorrectly calculated total was 58.5 × 30 = 1755.
The correction in the total is 75 − 57 = 18, so the corrected total is 1755 + 18 = 1773.
Therefore, the corrected mean is 1773 ÷ 30 = 59.1.
Cross-check
The mean must increase by 18 ÷ 30 = 0.6. Hence, 58.5 + 0.6 = 59.1, which confirms the result.