Higher January 2022 Paper 2 Q9
9 The frequency table gives information about the number of points scored by a player.
| Number of points | Frequency |
|---|---|
| 0 | 13 |
| 1 | 17 |
| 2 | 8 |
| 3 | \(x\) |
| 4 | 11 |
The mean number of points scored is 2
Work out the value of \(x\)
(4)
| Scheme | Marks |
|---|---|
| \((0 \times 13) + 1 \times 17 + 2 \times 8 + 3x + 4 \times 11\) or \((0 +)\;17 + 16 + 3x + 44\;(= 77 + 3x)\) | M1 |
| \((13 + 17 + 8 + x + 11)\) oe eg \(49 + x\) or \(98 + 2x\) | M1 |
| \(\dfrac{\text{``}{77 + 3x}\text{''}}{\text{``}{49 + x}\text{''}} = 2\) oe e.g. \(\text{``}{77 + 3x}\text{''} = 2(\text{``}{49 + x}\text{''})\) | M1 |
| 21 | A1 |
| (4) | |
| (4 marks) |
Notes
M1: at least 3 correct products with intention to add.
eg award for 77 seen as this is sum of 3 products
M1: Sum for total frequency or (frequency × 2)
M1: for use of mean in valid equation
(ft their values for sum of products and their total frequency if M2 awarded previously)