4MA0 Foundation June 2013 Paper 1R Q18
18 The table shows information about the time, in minutes, spent on homework by each of 32 pupils in one night.
| Time (\(t\) minutes) | Number of pupils |
|---|---|
| \(0 \lt t \leqslant 20\) | 7 |
| \(20 \lt t \leqslant 40\) | 16 |
| \(40 \lt t \leqslant 60\) | 3 |
| \(60 \lt t \leqslant 80\) | 6 |
(a) Calculate the percentage of the 32 pupils who spent more than 60 minutes on their homework. (2)
(b) Calculate an estimate for the total time spent on homework by the 32 pupils. (3)
| Scheme | Marks |
|---|---|
| \(\dfrac{6}{32} \times 100\) | M1 |
| 18.75 | A1 |
| (2) |
Notes
M1: Allow "32" from evidence of adding frequencies
A1: Accept 19 if the correct method or 18.75 seen
| Scheme | Marks |
|---|---|
| \((7 \times 10) + (16 \times 30) + (3 \times 50) + (6 \times 70)\) \(= 70 + 480 + 150 + 420\) | M1 M1(dep) |
| 1120 | A1 |
| (3) |
Notes
M1 M1(dep): M1 \(f \times x\) for 3 products with \(x\) used consistently within interval (inc. end points) & intention to add
M1(dep) use of correct half way values (\(\dfrac{1120}{32}\) implies M2)