Higher June 2023 Paper 4 Q6
6 A six-sided numbered spinner is thrown 50 times.
The score for each throw is recorded.
Some of the results are shown in the table.
An 8 was thrown \(f\) times.
An unknown number on the spinner is represented by \(n\).
| Score | Frequency |
|---|---|
| 1 | 12 |
| 3 | 2 |
| 5 | 9 |
| 6 | 16 |
| 8 | \(f\) |
| \(n\) | 4 |
| Total | 50 |
The mean score of the 50 throws is 5.5 .
Find the value of \(f\) and the value of \(n\). [4]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| [\(f\) =] 7 [\(n\) =] 15 | 4 | B1 for [\(f\) =] 7 AND B3 for [\(n\) =] 15 or M2 for 50 × 5.5 – (1 × 12 + 3 × 2 + 5 × 9 + 6 × 16 + 8 × their 7) [÷ 4] or better or forming an equation and attempting to solve it correctly e.g. (1 x 12)+(3 x 2) + (5 x 9) + (6 x16) + (8 x their f) +( \(n\) x 4) = 5.5 x 50 or better or M1 for 50 × 5.5 or 275 or 1 × 12 + 3 × 2 + 5 × 9 + 6 × 16 + 8 × their 7 or 215 | Note : if \(f\) is an error FT their f for the M marks M2 implied by 60 or 275 – their 215 better = 12 + 6 + 45 + 96 + their 56 Common error is 1 + 3 + 5 + 6 + 8 = 23 5.5 × 6 = 33 and 33 – 23 =10 scores M0 |