1MA0 Higher June 2015 Paper 2 Q14
14 Sumeet records the times, in minutes, for 40 runners to finish a half marathon.
Information about these times is shown in the table.
| Time (\(t\) minutes) | Frequency |
|---|---|
| \(60 \lt t \leqslant 90\) | 10 |
| \(90 \lt t \leqslant 120\) | 14 |
| \(120 \lt t \leqslant 150\) | 9 |
| \(150 \lt t \leqslant 180\) | 5 |
| \(180 \lt t \leqslant 210\) | 2 |
Calculate an estimate for the mean time. (4)
| Working | Answer | Mark | Notes |
|---|---|---|---|
| \(10 \times 75 + 14 \times 105 + 9 \times 135 + 5 \times 165 + 2 \times 195\) \(750 + 1470 + 1215 + 825 + 390\) \(4650 \div 40\) | 116.25 | 4 | M1 for finding at least 4 products ft consistently within interval (including end points) M1 (dep) for use of at least 4 correct midpoints. M1 (dep on 1st M) for \(\text{'}\Sigma ft\text{'} \div 40\) A1 for 116.25 |