Correcting Calculation Errors to Determine True Average Marks

When handling large datasets, even a single mistake can skew the results. In this article, we will explore a scenario where a tabulator incorrectly entered a score, leading to a misreported average. We will walk you through the steps to identify and correct the error, ensuring that the true average marks of the students are accurately calculated.

Scenario Description

During the process of calculating the average marks of 100 students, a tabulator accidentally entered 68 instead of the correct score, 86, leading to the reported average of 58. This discrepancy highlights the importance of maintaining accurate records and the impact such errors can have on final results. Let's understand the steps to find the actual average marks for these students.

Calculating Incorrect Total Marks

The initial step is to calculate the total marks using the incorrect score. Given that the average with the incorrect entry was 58, and the number of students is 100, we can derive the total marks as follows:

Let n represent the number of students. The given average with the incorrect entry is 58, so:

[ text{Total marks with incorrect entry} text{Average} times text{Number of students} 58 times 100 5800 ]

Adjusting the Total Marks

Next, we need to correct the total marks to reflect the actual score. The incorrect entry was 68, and the correct score should be 86. The difference between these values is:

[ text{Difference} 86 - 68 18 ]

Adding this difference to the incorrect total gives the actual total marks for the 100 students:

[ text{Actual total marks} 5800 18 5818 ]

Calculating the Actual Average

Finally, we calculate the actual average marks by dividing the corrected total marks by the number of students:

[ text{Actual average} frac{text{Actual total marks}}{text{Number of students}} frac{5818}{100} 58.18 ]

Thus, the true average marks of the students, after correcting the error, is 58.18.

Exploring Alternative Scenarios

Alternatively, we can use a variable to represent the total score of the students that were entered correctly:

Let X be the total score of the other students which were entered correctly. Then the equation becomes:

[ X 68 58 times 100 ]

Subtracting 68 from both sides, we get:

[ X 5800 - 68 5732 ]

Adding the correct score of the unfortunate student:

[ text{Actual total marks} 5732 86 5818 ]

The actual average can then be calculated as:

[ text{Actual average} frac{5818}{100} 58.18 ]

Impact of Error on Average

The error in the tabulator's entry reduced the total marks by 18. This means the original average (which included the incorrect score) was 0.18 less than the actual average. Adding this 0.18 back into the incorrect average of 58 gives us the true average:

[ text{Corrected average} 58 0.18 58.18 ]

Conclusion

Accurately calculating the average marks of a large group of students is crucial for fair and reliable assessments. This example underscores the importance of verification and correction processes to ensure that the final results reflect reality. By taking the time to identify and rectify such errors, educators and administrators can maintain the integrity of their assessment systems.