The average marks of 30 students in a maths test were found to be 55. However, it was later discovered that a mark of 72 was mistakenly recorded as 27, and another mark of 64 was mistakenly recorded as 46. What is the actual average score?

After correcting the mistakes in the recorded scores, the total marks of the 30 students increased from 1650 to 1713. The new average score is calculated to be 57.1. Hence, the actual average score of the students is 57.1.
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Answered by Anonymous | 2025-07-15

To find the correct average marks, we first need to correct the errors in the recorded marks.
Here are the steps to do this:

Initial Information :

The average mark of 30 students was initially given as 55.
Number of students, n = 30 .
Initial total marks = Average × Number of students = 55 × 30 = 1650 .


Corrections in Recorded Marks :

One student's mark of 72 was mistakenly recorded as 27.
Another student's mark of 64 was mistakenly recorded as 46.


Calculate the Correct Marks :

First correction: The mistake was 72 − 27 = 45 .
Second correction: The mistake was 64 − 46 = 18 .
Therefore, the total correction needed = 45 + 18 = 63 .


Correct Total Marks :

Correct total marks = Initial total marks + Total correction.
Correct total marks = 1650 + 63 = 1713 .


Find the Correct Average :

Correct average marks = Correct total marks / Number of students.
Correct average marks = 30 1713 ​ ≈ 57.1 .



Therefore, the actual average score is approximately 57.1.

Answered by BenjaminOwenLewis | 2025-07-22