The average marks of 72 students is shown as 69. It includes a wrong entry of 45 marks instead of 54 marks. The correct average is:
- A68.875 marks
- B69.125 marks
- C68.625 marks
- D69.375 marks
Solution & Step-by-step Explanation
Number of students = 72
Incorrect average = 69
Let us find the difference between the correct entry and the incorrect entry:
Difference=Correct value−Incorrect value=54−45=+9
Since the correct value is greater, the total sum must increase by 9.
The change in average due to this correction is:
Change in average=
Total number of students
Difference
=
72
9
=
8
1
=0.125
Therefore, the correct average is:
Correct average=Incorrect average+Change=69+0.125=69.125 marks
Incorrect average = 69
Let us find the difference between the correct entry and the incorrect entry:
Difference=Correct value−Incorrect value=54−45=+9
Since the correct value is greater, the total sum must increase by 9.
The change in average due to this correction is:
Change in average=
Total number of students
Difference
=
72
9
=
8
1
=0.125
Therefore, the correct average is:
Correct average=Incorrect average+Change=69+0.125=69.125 marks