Question : The average mark of 50 students in an examination was 65. It was later found that the marks of one student had been wrongly entered as 83 instead of 38. The correct average is:
Option 1: 63.9
Option 2: 64.5
Option 3: 64.7
Option 4: 64.1
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Correct Answer: 64.1
Solution :
Average marks of 50 students = 65.
Total marks of the students = 50 × 65 = 3250
Difference by the wrong entry = 83 – 38 = 45
So, the actual total marks of the students = 3250 – 45 = 3205
Average = $\frac{\text{Sum of observations}}{\text{Total no. of observations}}$
Average marks of 50 students $=\frac{3205}{50}$ = 64.1
Hence, the correct answer is 64.1.
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