Numeracy Foundation November 2023 Unit 2 Q7
7. A report from a Saturday newspaper is shown below.
Mean rainfall for the last 5 days is 42 mm
Mid Wales had significant rainfall over the last 5 days.
40 mm of rain fell on Monday, 37 mm on Tuesday and 39 mm on Wednesday.
Thursday was the wettest day, when 48 mm of rain fell.
Rain fell again on Friday.
The mean rainfall per day for these 5 days was 42 mm.
(a) Calculate the rainfall for Friday.
You must show all your working. [3]
You must show all your working. [3]
Rainfall on Friday was …………………… mm
(b) It did not rain on Saturday or Sunday in this week.
Calculate the mean rainfall per day for the week. [2]
Calculate the mean rainfall per day for the week. [2]
Mean rainfall per day for the week is …………………… mm
| Scheme | Marks | Comments |
|---|---|---|
| 5 × 42 – (40 + 37 + 39 + 48) or 210 – 164 or equivalent OR 40 + 37 + 39 + 48 + ….. = 5 × 42 or 164 + … = 210 | M2 | May be shown in stages Allow missing brackets as the intention to subtract M1 for sight of any one of the following:
|
| (Friday) 46 (mm) | A1 | CAO. Do not award from incorrect working Answer space takes precedence Do not allow an embedded answer |
Alternative
The alternative methods are printed in italics in the mark scheme.
7(a) Alternative methods
| Scheme | Marks | Comments |
|---|---|---|
| (Difference from mean) 42 + 2 + 5 + 3 – 6 OR (Contributions to the mean each day) \(5 \times \left(42 - \dfrac{40}{5} - \dfrac{37}{5} - \dfrac{39}{5} - \dfrac{48}{5}\right)\) or equivalent ( = 5 × 9.2) | M2 | M1 for \(42 - \dfrac{40}{5} - \dfrac{37}{5} - \dfrac{39}{5} - \dfrac{48}{5}\) |
| (Friday) 46 (mm) | A1 | CAO. Answer space takes precedence |
| Scheme | Marks | Comments |
|---|---|---|
| 5 × 42 ÷ 7 or 210 ÷ 7 | M1 | Allow ‘their 46’ from (a) has been truncated or rounded, FT any of the following:
|
| 30 (mm) | A1 | Answer space takes precedence On FT, accept rounded or truncated answers provided working is shown |