4400 Higher June 2008 Paper 3 Q11
11 The table shows information about the pulse rates of 60 people, when they were resting.
| Pulse rate (\(p\) beats/min) | Frequency |
|---|---|
| \(50 \lt p \leqslant 60\) | 7 |
| \(60 \lt p \leqslant 70\) | 21 |
| \(70 \lt p \leqslant 80\) | 15 |
| \(80 \lt p \leqslant 90\) | 14 |
| \(90 \lt p \leqslant 100\) | 3 |
The cumulative frequency graph gives information about the pulse rates of the same 60 people, after they have exercised for ten minutes.

| Scheme | Marks |
|---|---|
| \(60 \lt p \leqslant 70\) | B1 |
| (1) |
Notes
B1: Accept 60-70
| Scheme | Marks |
|---|---|
| \(55 \times 7 + 65 \times 21 + 75 \times 15 + 85 \times 14 + 95 \times 3\) or 385 + 1365 + 1125 + 1190 + 285 or 4350 | M1 M1 |
| \(\dfrac{\text{“}4350\text{”}}{60}\) | M1 |
| 72.5 | A1 |
| (4) |
Notes
M1 M1: M1 for finding at least four products \(f \times x\) consistently within intervals (inc end points) and summing them
M1 (dep) for use of halfway values (55, 65, ... ) or (55.5, 65.5, ...)
M1: \(\dfrac{\text{“}4350\text{”}}{60}\) (dep on 1st M1) for division by 60 or for \(\dfrac{\text{“}4380\text{”}}{60}\) if 55.5, 65.5, ... used
A1: for 72.5
Award 4 marks for 73 if first two M marks awarded
| Scheme | Marks |
|---|---|
| 30 (or \(30\frac{1}{2}\)) indicated on graph or stated | M1 |
| 124 or 125 | A1 |
| (2) |
Notes
M1: for 30 (or \(30\frac{1}{2}\)) indicated on graph or stated
A1: Accept any value in range 124-125 inc eg 124, 124.5, 125
| Scheme | Marks |
|---|---|
| Use of \(p = 131\) on graph | M1 |
| \(\approx 12\) | A1 |
| (2) | |
| (9 marks) |
Notes
M1: for use of \(p = 131\) shown on graph or implied by 47, 48 or 49 stated
A1: Accept any value in range 11-13 inc