Higher January 2019 Paper 2 Q13
13 The frequency table gives information about the numbers of mice in some nests.
| Number of mice | Frequency |
|---|---|
| 5 | 4 |
| 6 | 13 |
| 7 | 16 |
| 8 | \(x\) |
| 9 | 6 |
The mean number of mice in a nest is 7
Work out the value of \(x\).
(4)
| Scheme | Marks |
|---|---|
| \(4 \times 5 + 13 \times 6 + 16 \times 7 + 8x + 6 \times 9\) \((20 + 78 + 112 + 8x + 54)\) or \(264 + 8x\) | M1 |
\((4 + 13 + 16 + 6 + x) \times 7\) (\(= 7(39 + x) = 273 + 7x\)) or \((4 + 13 + 16 + 6) \times 7\) (=273) oe or \(\dfrac{\text{``}{264 + 8x}\text{''}}{\text{``}{39 + x}\text{''}}\) | M1 |
\(\dfrac{\text{``}{264 + 8x}\text{''}}{\text{``}{39 + x}\text{''}} = 7\) oe eg \(\text{``}{264 + 8x}\text{''} = \text{``}{(39 + x)}\text{''} \times 7\) or \(\text{``}{273}\text{''} - \text{``}{264}\text{''}\) | M1 |
| 9 | A1 |
| (4) | |
| (4 marks) |
Notes
M1: at least 3 products correct with intention to add
M1: for use of mean