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Question
The mean of marks scored by 100 students was found to be 40, later on, it was discovered that a score of 53 was misread as 83. Find the correct mean.
Solution
Total number of students = 100
Initial mean = 40
We first calculate the total sum of marks based on the initial mean:
Total Sum of Marks = Mean × Number of Students
Total Sum of Marks = 40 × 100 = 4000
A score of 53 was mistakenly read as 83.
The error introduced an extra 83 − 53 = 30 marks to the total.
To correct the total, subtract this error:
Correct Total Sum = Initial Total Sum − 30
Correct Total Sum = 4000 − 30 = 3970
The correct mean is calculated by dividing the corrected total sum by the number of students:
Correct Mean = `"Correct total Sum"/"Number of Students"`
Correct Mean = `3970/100`
= 39.7
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