Numeracy Higher November 2021 Unit 2 Q2
2. On Monday, Mrs Griffin recorded the time each of her students took to start a task.
She records her data in groups of equal width.
Mrs Griffin displays the results in a frequency polygon, as shown below.
(a) On Monday, how many students started the task? [2]
(b) In which group is the median time taken to start the task? [2]
(c)
Mrs Griffin had set a target that students should start the task within 30 seconds.
Was the target met?
You must give a reason for your answer. [1]
Yes ☐ No ☐ Can’t tell ☐
(d)
On Tuesday, the same students started the same task again.
25% of them started the task within 10 seconds.
Is this an improvement on the number of students who started the task within 10 seconds on Monday?
You must show all your working. [2]
Yes ☐ No ☐
| Scheme | Marks | Comments |
|---|---|---|
| 37 + 34 + 20 + 28 + 21 | M1 | Allow M1 for
|
| 140 (students) | A1 | Mark final answer |
| Scheme | Marks | Comments |
|---|---|---|
| 10 (seconds) to 15 (seconds) | B2 | Allow if considering the 0.5(n+1)th term throughout FT ‘their 140’ provided ‘their 140’ > 100 throughout Not from incorrect working Allow for an inclusive or exclusive range of times B1 for any of the following:
|
| Scheme | Marks | Comments |
|---|---|---|
| Selects or unambiguously implies ‘Yes’ with a reason, e.g. ‘no students in group 30 to 35 seconds’, ‘last students started in 25 to 30 second range’ | E1 | Allow the term ‘finished’ as meaning ‘finished starting the task’, e.g. ‘Yes’ with ‘no student finished after 30 seconds’ Allow, ‘yes’ with a reason, e.g. ‘all students started before 30 seconds’, ‘data stopped after 30 seconds’, ‘no students in the last group’ Allow selection of ‘Can’t tell’ with a reason based on thinking 30 seconds may be included in the group 25 to 30, so some students could have taken exactly 30 seconds to start and not started within 30 seconds, that is thinking ‘within 30 seconds’ does not include ‘30 seconds’ Do not accept ‘Yes’ with a reason, e.g. ‘no students after 27.5 seconds’, ‘all students between 27.5 and 32.5 seconds could start within 30 seconds’ |
| Scheme | Marks | Comments |
|---|---|---|
| \(\dfrac{37}{140}\) (× 100) or 0.25 × 140 or 0.25 × (37 + 34 + 20 + 28 + 21) or \(\dfrac{37}{37 + 34 + 20 + 28 + 21}\) (× 100) | M1 | FT ‘their derived 140’ from (a) provided >100 with numerator 37 or ‘their 37’ if seen in (a) |
| 26(.42...%) or 35 (students) AND ‘No’ indicated | A1 | Accept 0.26(...) only if 0.25 is seen |