Higher June 2022 Paper 2 Q1
1. The table shows the mass of 90 carrots grown by a gardener.
| Mass, \(m\) (grams) | Number of carrots |
|---|---|
| \(30 \lt m \leqslant 60\) | 9 |
| \(60 \lt m \leqslant 90\) | 33 |
| \(90 \lt m \leqslant 120\) | 38 |
| \(120 \lt m \leqslant 150\) | 8 |
| \(150 \lt m \leqslant 180\) | 2 |
Calculate an estimate for the mean mass of these carrots. [4]
| Scheme | Marks | Comments |
|---|---|---|
| Mid-points: 45, 75, 105, 135, 165 | B1 | May be implied from correct totals, see below |
| \(45 \times 9 + 75 \times 33 + 105 \times 38 +{}\) \(135 \times 8 + 165 \times 2\) | M1 | FT ‘their mid-points’ provided at least 4 of these are at the bounds or within the groups 405 + 2475 + 3990 + 1080 + 330 (= 8280) If mid-points are not given then no marks except for the following cases:
|
| \(\div\, 90\) | m1 | |
| 92 (grams) | A1 | FT correct evaluation using their mid-points Allow truncated or rounded decimal answers |
| (4) |