Foundation June 2018 Paper 2 Q22
22. The tourist office in Trofenberg displays the snowfall data each month in a table.
The table shows snowfall in Trofenberg for each day during January.
| Snowfall, \(s\) (cm) | Number of days |
|---|---|
| \(0 \leqslant s \lt 20\) | 1 |
| \(20 \leqslant s \lt 40\) | 8 |
| \(40 \leqslant s \lt 60\) | 9 |
| \(60 \leqslant s \lt 80\) | 7 |
| \(80 \leqslant s \lt 100\) | 6 |
(a) Calculate an estimate for the mean daily snowfall in Trofenberg for January.
You must show all your working. [4]
You must show all your working. [4]
(b)
There were 9 days when the snowfall was between 40 cm and 60 cm.
On each of these days, the snowfall was actually between 57 cm and 59 cm.
Explain why the estimate for the mean daily snowfall in January may still be fairly accurate. [1]
| Scheme | Marks | Comments |
|---|---|---|
| Midpoints 10, 30, 50, 70, 90 | B1 | |
| 1×10+8×30+9×50+7×70+6×90 | M1 | FT ‘their midpoints’ provided these are at the bounds or within the groups (10 + 240 + 450 + 490 + 540 = 1730) |
| ÷ 31 | m1 | |
| 55.8(…cm) | A1 | Accept 56(cm) from correct working |
| Scheme | Marks | Comments |
|---|---|---|
| Argument presented to include that (some) other groups could have snowfall towards the lower end of the group, e.g. ‘group 20 to 40 (cm) may have actual snowfall between 21 and 23 cm’ | E1 | Accept ‘the mean changes by about 2(.3 cm), so still about the same’ Allow, e.g. ‘Would not impact on the mean much’ Do not allow an argument presented saying ‘do not know the actual snowfall for the other groups’ Do not accept an argument based on the reason for using midpoints without further clarification |
| (5) |