The following table gives the percentage of marks obtained by seven students…
2023
The following table gives the percentage of marks obtained by seven students in six different subjects in an examination. The numbers in the brackets give the maximum marks in each subject.
What are the average marks obtained by all the seven students in Physics? (rounded off to two digits after the decimal)
- A.
77.26
- B.
89.14
- C.
91.37
- D.
96.11
Show answer & explanation
Correct answer: B
Concept: when a student's marks in a subject are reported as a percentage of that subject's own maximum marks, the actual marks equal (percentage x maximum marks) / 100. Since this scaling factor is the same maximum for every student in a given subject, the average of the marks equals the average of the percentages scaled by that same maximum: average marks = (average percentage) x (maximum marks) / 100.
Application (Physics, maximum marks = 120):
Read the Physics percentage of each of the seven students from the table: Ayush 90, Aman 80, Sajal 70, Rohit 80, Muskan 85, Tanvi 65, Tarun 50.
Sum the seven percentages: 90 + 80 + 70 + 80 + 85 + 65 + 50 = 520.
Divide the sum by the number of students to get the average percentage: 520 / 7 = 74.2857...%.
Convert the average percentage to marks using the Physics maximum of 120: 74.2857% x 120 / 100 = 89.14 (rounded to two decimals).
Cross-check: convert each student's percentage to actual Physics marks first, then average them directly - 90% of 120 = 108, 80% of 120 = 96, 70% of 120 = 84, 80% of 120 = 96, 85% of 120 = 102, 65% of 120 = 78, 50% of 120 = 60. Their sum is 108 + 96 + 84 + 96 + 102 + 78 + 60 = 624, and 624 / 7 = 89.14 - the same result as scaling the average percentage, confirming the calculation.
So the average marks obtained by all seven students in Physics is 89.14.