Numeracy Intermediate June 2025 Unit 2 Q10
10. 100 people took part in a fundraising event last Saturday and Sunday.
They raised money for charity by working towards some fitness targets.
The target for Saturday was to achieve a mean of 6500 steps per person.
The results for Saturday are shown in the table below.
| Number of steps | Number of people |
|---|---|
| 3001 to 5000 | 22 |
| 5001 to 7000 | 30 |
| 7001 to 9000 | 42 |
| 9001 to 11 000 | 6 |
Osian says,
“None of these 100 people recorded more than 10 000 steps on Saturday.”
Is this statement certainly true, not true, or is it not possible to tell?
You must give a reason for your answer. [1]
Certainly true ☐ Not true ☐ Not possible to tell ☐
On Sunday, the 100 people were divided into three groups, A, B and C, based upon their results from the Saturday.
Each group was given a target of a mean number of steps per person.
The targets for groups A, B and C were 8000, 9000 and 10 000 steps, respectively.
The table below shows the mean number of steps per person that each group achieved on Sunday.
| Group | A | B | C |
|---|---|---|---|
| Mean number of steps per person achieved | 5802 | 9830 | 12 200 |
The ratio of the number of people in the different groups was A : B : C = 18 : 4 : 3.
The organiser says,
“A fabulous result on Sunday! Two of the three groups met their target.
This means that two-thirds of the targets given were met.”
Give a reason why this could be seen as a misrepresentation of the outcome of Sunday’s fundraising event. [1]
| Scheme | Mark | Comments |
|---|---|---|
| (i) Midpoints: 4000.5, 6000.5, 8000.5, 10 000.5 | B1 | Accept 4000, 6000, 8000, 10 000 or 4001, 6001, 8001, 10 001 throughout |
| 22×4000(.5) + 30×6000(.5) + 42×8000(.5) + 6×10000(.5) (88011 + 180015 + 336021 + 60003 = 664050) (88000 + 180000 + 336000 + 60000 = 664000) | M1 | FT ‘their midpoints’ provided at least 3 lie within the appropriate group, including bounds throughout |
| ÷ 100 | m1 | |
| 6640(.5 steps) | A1 | Accept 6641 (steps) provided not from incorrect working ISW |
| (ii) ‘Not possible to tell’ unambiguously selected AND an appropriate reason, e.g. ‘don’t know how many steps the people in the last group actually did’, ‘some of the 6 people in the last group might have done more than 10 000 steps’ | E1 | Ignore additional incorrect or spurious statements Allow ‘Not possible to tell’ with the reason, e.g.: ‘don’t know the number of steps people did’, ‘grouped data’, ‘data is grouped’, ‘exact data not given’, ‘data is not specified’, ‘it doesn’t specify how many of the 6 people did 10 000 steps’, ‘it doesn’t specify how many people did 10 000 steps’ ‘it shows 6 people in the group 9001 to 11 000 steps’, ‘6 people walked between 9001 and 11 000 steps’, ‘any of the 6 in the group 9001 to 11 000 could have done 10 000’, ‘it shows 6 people did more than 9001 but less than 11 000’ ‘we don’t know how many steps they did accurately’, ‘the number of steps category goes above 10 000’, ‘someone in the last group may not know exactly how many steps they did’ Do not accept, ‘Not possible to tell’ with a reason, e.g. ‘it is only an estimate’, ‘the maximum is 11 000 steps’ |
| Scheme | Mark | Comments |
|---|---|---|
| (i) (18 × 5802 + 4 × 9830 + 3 × 12200) ÷ 25 or (4×18×5802 + 4×4×9830 + 4×3×12200) ÷ 100 | M2 | (= (104436 + 39320 + 36600) ÷ 25 = 180356 ÷ 25) (= (417744 + 157280 +146400) ÷100 = 721424÷100) M1 for any one of the following:
|
| 7214(.24 steps) | A1 | Allow 7215 provided not from incorrect working |
| (ii) Suitable reason, e.g. ‘majority of the people were in the group that didn’t meet their target’, ‘72% were in the group that didn’t achieve the target’, ‘only 28% (or \(\dfrac{7}{25}\)) of the people were in the two groups that met their target’ | E1 | Ignore additional incorrect or spurious statements Allow, e.g. ‘most of the people didn’t meet their target’, ‘more people in group A’, ‘2 of the 3 groups does not mean two thirds’, ‘data is grouped, we don’t know how many people met the target’, ‘there is not an equal number of people in each group’, ‘different number of people in each group’, ‘different amounts in each group’ Do not accept, e.g. ‘groups B and C met their target’, ‘some people in a group could have met the target but others didn’t’, ‘because 5802 out of 8000 in group A’, ‘because there were more people in the group’, ‘the group that did not meet their target could be a long way from their target’, ‘they don’t say which groups reached their targets’, ‘they were grouped into different capabilities’, ‘it only shows the mean for each of the 3 groups’, ‘data is grouped’, ‘not all the targets were the same’, ‘group A did not reach their target’ |