Higher November 2022 Paper 6 Q17
17 Charlie weighs many apples.
The weights of the apples are summarised below.
- heaviest apple = 75 g
- range = 50 g
- median = 60 g
- lower quartile = 45 g
- 50% of the apples weigh between 45 g and 65 g
- mean = 63 g
(a)
(i) Write down the interquartile range for the weights of the apples, in g. [1]
(ii) Write down the percentage of the apples that weigh between 45 g and 60 g. [1]
(b) Draw a box plot to show the distribution of the weights of the apples.
(c) Charlie eats two of the apples.
The apples that they eat weigh 58 g and 66 g.
The apples that they eat weigh 58 g and 66 g.
Charlie says
The mean weight of all the apples was 63 g.
I ate one apple that weighed less than the mean and another apple that weighed more than the mean.
Therefore, the mean of the remaining apples will still be 63 g.
Is Charlie correct?
Explain your reasoning. [2]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| (a)(i) | |||
| 20 | 1 | ||
| (a)(ii) | |||
| 25 | 1 | ||
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| Box plot drawn with: Lowest = 25 Lower Quartile = 45 Median = 60 Upper quartile = 65 Highest = 75 | 3 | B2 for 4 or 5 correct markers or B1 for 3 correct markers | If more than 5 markers, mark the worst 5 Award the markers even if not correctly representing the information |
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| Calculation/reasoning/use of figures | 1 | See Appendix | |
| Correct interpretation | 1dep | ||
Appendix Q17(c)
Use of figures or reasoning needed to score any marks
Use of figures or reasoning may be 1 mark. Interpretation is dependent on figures/reasoning
| Response | Reason | Mark |
|---|---|---|
| (58+66)/2=62. Incorrect, new mean will be more than 63. | Useful calculation; correct interpretation | 2 |
| (58+66)/2=62. Incorrect, new mean will be less than 63. | Useful calculation; wrong interpretation | 1 |
| (58+66)/2=62. | Useful calculation | 1 |
| Incorrect. The mean of the two apples is 62, so the mean of the remaining apples will rise. | Implied calculation; correct interpretation | 2 |
| 63-58=5; 66-63=3. Incorrect, new mean will be more than 63. | Useful calculation; correct interpretation | 2 |
| 63-58=5; 66-63=3. Incorrect, new mean will be less than 63. | Useful calculations; wrong interpretation | 1 |
| 63-58=5; 66-63=3. | Useful calculations | 1 |
| If there were 10 apples, then new mean = (63 × 10 - 58 - 66)/8 = 63.25. The mean would increase | Useful calculation; correct interpretation | 2 |
| Useful figures/calculations/reasoning and “no” | “No” is insufficient interpretation | 1 |
| Useful figures/calculations/reasoning and “the mean will change” | The interpretation is equivalent to “no” | 1 |
| Mean will be smaller because Charlie ate 2 apples | Insufficient use of figures | 0 |
| No, because the total weight and the number of apples have changed | No calculations/reasoning/use of figures. | 0 |
| No, the mean will change | No calculations/reasoning/use of figures. | 0 |