4MA0 Higher January 2016 Paper 3 Q13
13 Here are the marks that James scored in eleven maths tests.
16 12 19 18 17 13 13 20 11 19 17
(a) Find the interquartile range of these marks. (3)
Sunil did the same eleven maths tests.
The median mark Sunil scored in his tests is 17
The interquartile range is 8
(b) Which one of Sunil or James has the more consistent marks?
Give a reason for your answer. (1)
Give a reason for your answer. (1)
Sunil did four more maths tests.
His scores in these four tests were 16, 20, 18 and 10
(c) How does his new median mark for the fifteen tests compare with his median mark of 17 for the eleven tests?
Tick (✓) one box.
Tick (✓) one box.
- new median is lower
- new median is 17
- new median is higher
| Scheme | Marks |
|---|---|
| 11 12 13 13 16 17 17 18 19 19 20 | M1 |
| 11 12 13 13 16 17 17 18 19 19 20 or 19 −13 | M1 |
| 6 | A1 |
| (3) |
Notes
M1: 13 or 12.75 (LQ)
19 or 18.25 (UQ) identified from ordered list
OR attempt to find IQR eg.
3(rd) and 9(th) seen or
2.75(th) and 8.25(th) seen
M1: Identify
13 or 12.75 (LQ),
AND
19 or 18.25 (UQ)
A1: accept 5.5
| Scheme | Marks |
|---|---|
| James and reason using IQR | B1 |
| (1) |
Notes
B1: ft from (a) James - he has a lower IQR oe
(IQR must be part of the statement)
| Scheme | Marks |
|---|---|
| no change with reason | B1 |
| (1) |
Notes
B1: no change box ticked with reason eg. 2 new scores above median and 2 new scores below median or median of 4 numbers is 17