Foundation November 2020 Paper 3 Q4
4 A teacher asks nine of his pupils how many pets they have at home.
Here are the results.
1 1 1 2 3 4 5 7 111
(a) Work out the range of the nine results. [1]
(b) The median of the nine results is 3.
The mean is 15.
The mean is 15.
(i) Write down the mode. [1]
(ii) The teacher wants to use a sensible average to summarise the results.
Which average should he use and why?
.................. because .................. [1]
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| 110 | 1 | ||
| Answer | Marks | Part marks and guidance | |
|---|---|---|---|
| (i) 1 | 1 | ||
| (ii) Median [because] All but one score is close to 3 oe | 1 | Allow, it is not distorted by (the high value or 111) oe Accept 3 for Median Must mention or imply clustering or distortion See Appendix | |
Appendix
Exemplar responses for Q4b(ii)
| Response | Mark | |
|---|---|---|
| Mode. It is the most common number of pets | Defines mode | 0 |
| Median It’s the middle number | Defines median | 0 |
| Mean It would include all the numbers | Doesn’t recognise distortion | 0 |
| 3 We don’t include 111 in the calculation. It’s an anomaly | Doesn’t mention distortion | 0 |
| Median It is a realistic figure | Doesn’t say why it is realistic | 0 |
| Median [It’s the more realistic average as] most pupils are closest to 3 than the rest | Implies clustering | 1 |
| 3 Most of the numbers are near this | Accept 3 for Median (and imply Mode from 1) | 1 |