4400 Higher June 2005 Paper 3 Q10
10 The table gives information about the ages, in years, of the 80 members of a sports club.
| Age (\(t\) years) | Frequency |
|---|---|
| \(10 < t \leqslant 20\) | 8 |
| \(20 < t \leqslant 30\) | 38 |
| \(30 < t \leqslant 40\) | 28 |
| \(40 < t \leqslant 50\) | 4 |
| \(50 < t \leqslant 60\) | 2 |
| Age (\(t\) years) | Cumulative frequency |
|---|---|
| \(10 < t \leqslant 20\) | |
| \(10 < t \leqslant 30\) | |
| \(10 < t \leqslant 40\) | |
| \(10 < t \leqslant 50\) | |
| \(10 < t \leqslant 60\) |
(1)

(2)
Show your method clearly. (2)
| Scheme | Marks |
|---|---|
| 15 × 8 + 25 × 38 + 35 × 28 + 45 × 4 + 55 × 2 = 120 + 950 + 980 + 180 + 110 = 2340 | M1 M1 |
| 2340 ÷ 80 | M1 |
| 29.25 | A1 |
| (4) |
Notes
M1: For products \(m \times f\) where \(m\) is consistent inc end points
M1: (dep) for use of midpoints (15, 25, … or 15.5, 25.5, …)
M1: (dep on 1st M1) for adding and ÷ 80
A1: Accept 29, 29.2, 29.3 if first two M1s scored (If 15.5, 25.5, … used, mean = \(\frac{2380}{80}\) = 29.75)
| Scheme | Marks |
|---|---|
| 8, 46, 74, 78, 80 | B1 |
| (1) |
Notes
B1: cao
| Scheme | Marks |
|---|---|
| Points correct | B1 |
| Curve or line segments | B1 |
| (2) |
Notes
B1: ±½ sq ft from sensible table
B1: ft from points if 4 or 5 points correct or if points are plotted consistently within each interval at the correct heights
| Scheme | Marks |
|---|---|
| use of 40 (or 40.5) on graph or 40th (or 40.5th) stated | M1 |
| ~29 | A1 |
| (2) | |
| (9 marks) |
Notes
M1: For use of 40 (or 40.5) on graph or 40th (or 40.5th) stated
A1: If M1 scored, ft from cumulative frequency graph
If no working, follow through only from correct curve