Higher November 2017 Paper 2 Q3
3. The table shows the daily rainfall in Hightown during September 2017.
| Rainfall, \(r\) mm | Number of days |
|---|---|
| \(0 \leqslant r \lt 4\) | 4 |
| \(4 \leqslant r \lt 6\) | 14 |
| \(6 \leqslant r \lt 10\) | 10 |
| \(10 \leqslant r \lt 14\) | 2 |
(a) Calculate an estimate of the mean daily rainfall in Hightown for September 2017. [4]
(b) The actual mean daily rainfall in Seabank during September 2017 was 5·9 mm.
Explain how it is possible that the actual mean daily rainfall in Hightown and Seabank were both the same for September 2017. [1]
Explain how it is possible that the actual mean daily rainfall in Hightown and Seabank were both the same for September 2017. [1]
| Scheme | Marks | Comments |
|---|---|---|
| Midpoints 2, 5, 8, 12 | B1 | |
| \(2\times4 + 5\times14 + 8\times10 + 12\times2\) | M1 | FT ‘their midpoints’ provided these are at the bounds or within the groups (8 + 70 + 80 + 24 = 182) |
| \(\div\ 30\) | m1 | |
| 6(.0666…mm) | A1 |
| Scheme | Marks | Comments |
|---|---|---|
| Explanation, e.g. ‘Hightown is only an estimate’, ‘Hightown mean was calculated using midpoints’, ‘more of the Hightown results might be below the midpoints’ | E1 | Accept a suitable example |
| (5) |