Question

The average marks of 50 students in a class was found to be 64. If the marks of two students were incorrectly entered as 38 and 42 instead of 83 and 24, respectively, then what is the correct average?

• A. 64.54
• B. 62.32
• C. 61.24
• D. 61.86

Hint:

To find the correct average when an error in data entry occurs, first compute the initial total sum, then correct the erroneous values by subtracting the incorrect ones and adding the correct ones.

Answer 1

The Correct Option is A

The total sum of marks of the 50 students initially is calculated using the average given: \[ {Total Marks} = 64 \times 50 = 3200 \] However, two students' marks were entered incorrectly. The incorrect entries were 38 and 42, instead of 83 and 24. To correct the total sum, we need to subtract the incorrect entries and add the correct ones. 1. Subtract the incorrect entries: \[ {Corrected Total} = 3200 - (38 + 42) = 3200 - 80 = 3120 \] 2. Add the correct entries: \[ {Corrected Total} = 3120 + (83 + 24) = 3120 + 107 = 3227 \] Now, to find the correct average: \[ {Correct Average} = \frac{3227}{50} = 64.54 \] Thus, the correct average is 64.54, making the correct answer Option A.