A student scores 55, 60, 65 and 70 respectively in English, Physics, Chemistry…
2020
A student scores 55, 60, 65 and 70 respectively in English, Physics, Chemistry and Mathematics. If the credits assigned to English, Physics, Chemistry and Mathematics are 2, 3, 3 and 4 respectively then what would be the average mark of the student?
- A.
62.50
- B.
63.75
- C.
64.25
- D.
64.75
Attempted by 9 students.
Show answer & explanation
Correct answer: B
Concept
The weighted average (weighted mean) is not the plain average of the marks. Each mark is multiplied by its own credit (weight), the products are summed, and that total is divided by the sum of all the credits. In symbols: weighted average = (Σ markᵢ × creditᵢ) / (Σ creditᵢ). Marks attached to larger credits therefore pull the result more strongly than marks with smaller credits.
Application
Multiply each mark by its credit: English 55 × 2 = 110, Physics 60 × 3 = 180, Chemistry 65 × 3 = 195, Mathematics 70 × 4 = 280.
Add the weighted products to get the total weighted score: 110 + 180 + 195 + 280 = 765.
Add the credits to get the total weight: 2 + 3 + 3 + 4 = 12.
Divide the total weighted score by the total credits: 765 ÷ 12 = 63.75.
Cross-check
As a sanity check, the plain (unweighted) average of 55, 60, 65, 70 is 250 ÷ 4 = 62.50. Because the highest marks (Chemistry 65 and Mathematics 70) carry the largest credits, the weighted result must sit above 62.50, and 63.75 does — confirming the value is reasonable. The weighted average of the student's marks is 63.75.