4MA0 Foundation June 2012 Paper 2 Q16
16 A group of students take a test.
The group consists of 12 boys and 8 girls.
The mean mark for the boys is 18
The mean mark for the girls is 16.5
Calculate the mean mark for the whole group.
(4)
| Scheme | Marks |
|---|---|
| (12 × 18) + (8 × 16.5) (=348) | M2 |
| “348” ÷ 20 | M1 |
| 17.4 | A1 |
| (4) | |
| (Total 4 marks) |
Notes
M2: M1 for 12 × 18 (=216) or 8 × 16.5 (=132)
M1: dep on at least 1 previous M1
Alt: Ratio method
| Scheme | Marks |
|---|---|
| 12:8 = 3:2 or 6:4 | M1 |
| 18×3 and 16.5×2 or 18 × 6 and 16.5 × 4 | M1 |
| (18×3 + 16.5×2) ÷ 5 or (18 × 6 + 16.5 × 4) ÷ 10 | M1 |
| 17.4 | A1 |
Alt: Proportion method
| Scheme | Marks |
|---|---|
| 60% boys and 40% girls stated or implied | M1 |
| (0.6 × 18) + (0.4 × 16.5) (= 10.8 + 6.6) | M2 |
| 17.4 | A1 |
Notes
M2: M1 for 0.6 × 18 or 0.4 × 16.5
SC B1 for 17.1 (from {(8 × 18) + (12 × 16.5)} ÷ 20)