Foundation November 2019 Paper 2 Q20
20.
(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.
| 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.
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 × 4 + 3 × 2 + 4 × 1 + 5 × 0 + 6 × 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 |
| ÷ 10 | m1 | |
| 3.6 (cm) | A1 |
| Scheme | Marks | Comments |
|---|---|---|
| 5 × 4.7 + 23.9 | M1 | |
| ÷ 6 | m1 | |
| 7.9 (cm) | A1 | |
| (8) |