Worked example · PE · Year 9
LNF: Numeracy → Learning that statistics represent data and that probability models chance helps us make informed inferences and decisions → Interpreting data
A secure Year 9 response, annotated so you can see which success criterion each part meets. It is also the answer key. Key figures: week 1 ratings Above average, Below average, Average, Average; class median 25 cm, mean 24.9 cm, range 24 cm; 8 of 15 (53.3%) Above average or Excellent; percentage changes 3.7%, 5.4%, 4.2%, 20.0%. The sprint moves from Below average to Average.
| Test | Week 1 result | Rating | Rank |
|---|---|---|---|
| Sit and reach | 27 cm | Above average (25 to 29) | 1 |
| 30 m sprint | 5.6 s | Below average (5.6 to 5.9) | 4 |
| Standing broad jump | 165 cm | Average (160 to 179) | 2 |
| Sit-ups in 60 s | 30 | Average (30 to 37) | 3 |
The sit-ups and broad jump are both Average, but 30 sit-ups is right at the bottom of its band, while 165 cm is 5 cm into its band, so the broad jump ranks higher.
Boundary: 30 sit-ups is Average, because the Average band is “30 to 37”, which includes 30. Below average stops at 29.
Every rating is correct, including the sprint, where 5.6 s is the fastest time in the Below average band but still Below average. The tie is broken with a reason. Evidences criterion 1.
(a) 12, 18, 19, 21, 22, 22, 24, 25, 26, 27, 28, 29, 31, 33, 36
| Working | Answer | |
|---|---|---|
| Median | 15 values, so the middle is the 8th value | 25 cm |
| Mean | Total 373 ÷ 15 = 24.866… | 24.9 cm |
| Range | 36 − 12 | 24 cm |
(c)
| Rating | Values | Frequency |
|---|---|---|
| Excellent (30 or more) | 31, 33, 36 | 3 |
| Above average (25 to 29) | 25, 26, 27, 28, 29 | 5 |
| Average (20 to 24) | 21, 22, 22, 24 | 4 |
| Below average (15 to 19) | 18, 19 | 2 |
| Poor (14 or less) | 12 | 1 |
| Total | 15 |
(d) 3 + 5 = 8 girls, and 8 ÷ 15 × 100 = 53.3%. Lowri’s 27 cm is above both the mean (24.9 cm) and the median (25 cm): she is in the top half of her class for flexibility.
The data is ordered before the median is found, the mean is rounded correctly, and the frequencies add up to 15. Total check: 22 + 31 + 18 + 27 + 25 + 12 + 29 + 24 + 36 + 21 + 26 + 33 + 19 + 28 + 22 = 373. Evidences criterion 2.
| Test | Week 1 | Week 7 | Change | Percentage change | Week 7 rating |
|---|---|---|---|---|---|
| Sit and reach | 27 cm | 28 cm | +1 cm | 1 ÷ 27 × 100 = 3.7% | Above average (no change) |
| 30 m sprint | 5.6 s | 5.3 s | 0.3 s faster | 0.3 ÷ 5.6 × 100 = 5.4% | Average (up from Below average) |
| Standing broad jump | 165 cm | 172 cm | +7 cm | 7 ÷ 165 × 100 = 4.2% | Average (no change) |
| Sit-ups in 60 s | 30 | 36 | +6 | 6 ÷ 30 × 100 = 20.0% | Average (near the top of the band) |
The sit-ups improved most, by 20.0%. That matches her plan: she did core exercises, including sit-ups, twice a week, more than anything else. The sprint, which she trained once a week, improved second most. Percentages are fairer than raw changes here, because the tests use different units: 7 cm and 0.3 s cannot be compared directly.
Each percentage divides by the week 1 value, and the sprint is correctly treated as an improvement even though the number went down. The pupil explains why percentages are needed. Evidences criterion 3.
(a) 1. Week 1 was outside on a wet, windy field and week 7 was in a sports hall, so the sprint and jump were probably easier in week 7. The conditions changed, not just her fitness. 2. A different friend timed the sprint each time, and stopwatch timing depends on reaction time, so 0.3 s could partly be timing error. Also, week 1 was her first timed sit-up test; she may have scored more in week 7 partly because she knew how to pace herself.
(b) Norms only compare you with other people of the same age and sex. They do not show what your own sport needs: a netball player and a long-distance runner need different fitness. Also, these norms are invented; real tables come from particular groups of people and may not match your school.
Both reasons come from the evidence in Lowri’s notes and explain how each could change the result. Evidences criterion 4.
In week 1, Lowri’s biggest strength was flexibility: her sit and reach of 27 cm was Above average and above the class median of 25 cm. Her biggest weakness was speed, with a Below average sprint of 5.6 s. After 6 weeks her sit-ups improved by 20.0% and her sprint by 5.4%, which moved it up to Average. She should now train leg power with jumping exercises, because her broad jump is still only Average, improved by just 4.2% and was not part of her plan. However, some of the sprint gain may not be real, because week 1 was on a wet, windy field and different friends timed her.
110 words. Strength and weakness named with ratings and figures, three percentages, a next step justified by the data and a limitation from the evidence. Evidences criterion 5.
Above average sprint: 5.1 s or faster. 5.3 − 5.1 = 0.2 s, and 0.2 ÷ 5.3 × 100 = 3.8%.
Mode: 22 cm, the only value that appears twice. It is less useful than the median because it depends on just 2 pupils, and it sits below the middle of the data.
Bar chart: five bars with heights 3, 5, 4, 2 and 1, labelled with the ratings, a vertical axis “Number of girls” from 0 to 5 and a title such as “Sit and reach ratings, Year 9 girls, week 1”.