Higher June 2024 Paper 2 Q13
13 Liam takes part in long jump competitions.
Here is some information about 40 of his jumps.
| Length of jump, \(d\) metres | Number of jumps | Midpoint | |
|---|---|---|---|
| \(7.0 \leqslant d \lt 7.4\) | 15 | ||
| \(7.4 \leqslant d \lt 7.8\) | 18 | ||
| \(7.8 \leqslant d \lt 8.2\) | 7 | ||
| Total \(= 40\) |
Work out an estimate of the mean distance of these 40 jumps.
Give your answer as a decimal. [3 marks]
| Answer | Mark | Comments |
|---|---|---|
| \(15 \times 7.2\) or 108 and \(18 \times 7.6\) or 136.8 and \(7 \times 8\) or 56 | M1 | oe implied by 300.8 allow one product or \(fx\) value to be incorrect |
| \((108 + 136.8 + 56) \div 40\) or \(300.8 \div 40\) or \(\dfrac{188}{25}\) | M1dep | oe do not allow if any exact \(fx\) or \(\Sigma fx\) value is approximated |
| 7.52 | A1 | accept 7.5 if 7.52 in working lines with no incorrect method |
Additional guidance
| M1 may be awarded for correct work with no answer or incorrect answer, even if this is seen amongst multiple attempts | |
| \(15 \times 7.2 \quad 18 \times 7.6 \quad 7 \times 8\) \((108 + 137 + 56) \div 40\) (\(fx\) value 137 is approximated) | M1 M0 |
| \(108 + 136.8 + 56 = 300.8\) \(300 \div 40\) (\(\Sigma fx\) value 300 is approximated) | M1 M0 |
| M1dep Missing brackets must be recovered eg \(108 + 136.8 + 56 \div 40\) not recovered | M1M0 |
| 7.52 in working with answer \(7.4 \leqslant d \lt 7.8\) | M2A0 |