Higher November 2019 Paper 2 Q5
5.
(a) In Queenbridge, the mean daily snowfall for a week was 1·6 cm.
If there had been 1 cm more snowfall on each day, what would the mean daily snowfall have been? [1]
If there had been 1 cm more snowfall on each day, what would the mean daily snowfall have been? [1]
(b) In Sansburg, the snowfall for each of the first 10 days in January was measured.
The results are summarised in the table below.
The results are summarised in the table below.
| Daily snowfall, \(s\) in cm | Number of days |
|---|---|
| \(1{\cdot}5 \leqslant s \lt 2{\cdot}5\) | 4 |
| \(2{\cdot}5 \leqslant s \lt 3{\cdot}5\) | 2 |
| \(3{\cdot}5 \leqslant s \lt 4{\cdot}5\) | 1 |
| \(4{\cdot}5 \leqslant s \lt 5{\cdot}5\) | 0 |
| \(5{\cdot}5 \leqslant s \lt 6{\cdot}5\) | 3 |
Calculate an estimate for the mean daily snowfall for these 10 days. [4]
(c) During the first 5 days of February, the mean snowfall in Awezell was 4·7 cm.
On 6th February the snowfall was 23·9 cm.
On 6th February the snowfall was 23·9 cm.
Calculate the mean snowfall for the first 6 days of February. [3]
| Scheme | Marks | Comments |
|---|---|---|
| 2.6 (cm) | B1 |
| Scheme | Marks | Comments |
|---|---|---|
| Mid points 2, 3, 4, 5, 6 | B1 | |
| \(2 \times 4 + 3 \times 2 + 4 \times 1 + 5 \times 0 + 6 \times 3\) | M1 | FT ‘their mid points’ provided 4 lie within, including ‘bounds’, of the groups, allow 1 of the mid points is outside the group |
| \(\div 10\) | m1 | |
| 3.6 (cm) | A1 |
| Scheme | Marks | Comments |
|---|---|---|
| \(5 \times 4.7 + 23.9\) | M1 | |
| \(\div 6\) | m1 | |
| 7.9 (cm) | A1 | |
| (8) |