Worked example · PE · Year 8
LNF: Numeracy → Learning that statistics represent data and that probability models chance helps us make informed inferences and decisions → Representing data
A secure Year 8 response, annotated so you can see which success criterion each part meets. It is also the answer key. Key figures: Elin 45 to 82 s, up 37 s (82.2%); Rhodri 70 to 83 s, up 13 s (18.6%); best scale 1 square = 10 s; outlier: Rhodri, week 3, 40 s.
| Week | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|---|---|---|
| Elin (s) | 45 | 52 | 50 | 61 | 68 | 66 | 75 | 82 |
| Rhodri (s) | 70 | 72 | 40 | 74 | 78 | 80 | 81 | 83 |
Every time is in one unit before plotting. Evidences criterion 1.
(a) 83 s. (b) 1 square = 10 seconds, so the axis goes from 0 to 120 and 83 s is 8.3 squares up. 5 seconds a square would only reach 60 s, which is too small, and 20 seconds a square would squash the lines into the bottom half. (c) 2 squares between weeks, so 8 weeks use 16 of the 18 squares.
The scale is chosen by checking the largest value against the size of the grid, and the pupil rules out two other options. Evidences criterion 2.
Title: Plank hold times for Elin and Rhodri over the 8-week challenge. (Drawn here with a line every 10 s, and the axis stopped at 90 s to save space.)
Both axes are labelled with units, the steps are equal, the points are joined with straight lines and a key tells the lines apart. Evidences criterion 3.
(a) Elin’s times rose steadily, from 45 s in week 1 to 82 s in week 8.
(b) From week 3 to week 4, when she improved by 11 s (50 s to 61 s). It is the steepest part of her line.
(c) Rhodri’s 40 s in week 3 is the outlier: it is 32 s lower than the week before, and he had a heavy cold. It should not count when judging his progress, because it shows his illness, not his fitness.
(d) Elin dips in weeks 3 and 6 (by 2 s each time). Both times, she was tested straight after a long netball practice and was already tired.
Trends are described with numbers, the steepest section is linked to the biggest change, and the outlier and dips are explained from the evidence. Evidences criterion 4.
| Week 1 (s) | Week 8 (s) | Improvement (s) | Percentage improvement | |
|---|---|---|---|---|
| Elin | 45 | 82 | 37 | 37 ÷ 45 × 100 = 82.2% |
| Rhodri | 70 | 83 | 13 | 13 ÷ 70 × 100 = 18.6% |
(b) Elin made much more progress. She improved by 37 s, an 82.2% increase, compared with Rhodri’s 13 s, 18.6%. Her line is much steeper and nearly catches his by week 8. Rhodri was already trained at rugby, so he had less room to improve, and he practised less at home.
(c) The data shows change over time, and a line graph shows the direction and speed of that change. A pie chart shows parts of a whole, and the weekly times are not parts of anything.
Percentages give a fair comparison between different starting points, and the choice of graph is justified by what the data is. Evidences criteria 4 and 5.
Rhodri’s mean: with week 3, 578 ÷ 8 = 72.3 s (72.25). Without week 3, 538 ÷ 7 = 76.9 s. The outlier pulls the mean down by about 4.6 s.
Elin’s week 10 target: about 90 to 95 s. Her line rises by about 5 s a week on average (37 ÷ 7 = 5.3 s), so 2 more weeks would add about 10 s to 82 s.