Worked example · Humanities · Year 6
LNF: Numeracy → Learning that statistics represent data and that probability models chance helps us make informed inferences and decisions → Interpreting data
A secure Year 6 response, annotated so you can see which success criterion each part meets. It is also the answer key. It uses the invented data on the stimulus sheet “Rainfall at two weather stations in Wales”. Headline answers: Station A total 2760 mm, mean 230 mm, range 210 mm; Station B total 900 mm, mean 75 mm, range 65 mm. Winter and summer: A 910 mm and 460 mm, B 280 mm and 170 mm. Chart 3 makes November look 14 times as wet as May, but it is really about 2.4 times. Step 6: true, cannot tell, false, cannot tell.
| # | Question | Answer | Tick |
|---|---|---|---|
| 1 | Station A in March (Chart 1) | 250 mm | ✓ |
| 2 | Station A month with exactly 300 mm (Chart 1) | October | ✓ |
| 3 | Station A in August (Chart 1) | 180 mm (3 faint lines above 150) | ✓ |
| 4 | Station B in August (Chart 2) | 65 mm (1 faint line above 60) | ✓ |
| 5 | Station B biggest rise (Chart 2) | September to October, up 25 mm (75 to 100) | ✓ |
Each value is read by counting the faint lines from the nearest labelled number, then checked against the table. In question 5 the pupil looks for the steepest line going up, not the steepest fall (January to February, down 25 mm). Evidences criterion 1.
| Station | Wettest month and amount | Driest month and amount | Range (mm) |
|---|---|---|---|
| A (Eryri) | January, 340 mm | June, 130 mm | 340 − 130 = 210 |
| B (Pembrokeshire) | November, 110 mm | May, 45 mm | 110 − 45 = 65 |
Station A’s rain changes much more from month to month. Its range is 210 mm, but Station B’s range is only 65 mm, so Station B’s months are much closer together.
Both the month and the amount are given, and the range is used to describe how spread out each data set is. Evidences criterion 2.
(a) Station A in pairs: 340 + 260 = 600, 250 + 160 = 410, 140 + 130 = 270, 150 + 180 = 330, 220 + 300 = 520, 320 + 310 = 630. Total: 600 + 410 + 270 + 330 + 520 + 630 = 2760 mm. Mean: 2760 ÷ 12 = 230 mm.
Station B in pairs: 100 + 75 = 175, 70 + 50 = 120, 45 + 50 = 95, 55 + 65 = 120, 75 + 100 = 175, 110 + 105 = 215. Total: 175 + 120 + 95 + 120 + 175 + 215 = 900 mm. Mean: 900 ÷ 12 = 75 mm.
| Station | Total for the year (mm) | Mean rain per month (mm) |
|---|---|---|
| A (Eryri) | 2760 | 230 |
| B (Pembrokeshire) | 900 | 75 |
(b) 3 × 900 = 2700. Station A got 2760 mm, which is only 60 mm more than 2700. So yes, Station A is about 3 times as wet as Station B. The means agree: 3 × 75 = 225, and 230 is close to 225.
(c) Station A got more than 230 mm in January (340), February (260), March (250), October (300), November (320) and December (310). That is 6 months. They are all in autumn, winter and early spring.
The totals are found with a clear method, the mean is worked out as total ÷ 12, and the mean is then used to compare the stations and to sort the months into wetter and drier than usual. Evidences criterion 3.
| Station | Winter total (mm) | Summer total (mm) | Difference (mm) |
|---|---|---|---|
| A (Eryri) | 310 + 340 + 260 = 910 | 130 + 150 + 180 = 460 | 910 − 460 = 450 |
| B (Pembrokeshire) | 105 + 100 + 75 = 280 | 50 + 55 + 65 = 170 | 280 − 170 = 110 |
At both stations, winter is wetter than summer. At Station A, winter is about 2 times as wet as summer, because 2 × 460 = 920, which is very close to 910.
Yes, it matches. The stimulus sheet says the west of Wales is usually wetter in autumn and winter than in spring and summer, and both stations in the west got more rain in winter than in summer.
The right 3 months are used for each season, and the totals are compared using both the difference and “times as much”. The conclusion is linked back to the real pattern. Evidences criteria 2 and 3.
(a) Chart 3 starts at 40 mm. A fair bar chart should start at 0.
(b) The November bar goes from 40 to 110, which is 14 faint lines of 5 mm. The May bar goes from 40 to 45, which is 1 faint line. So the November bar looks 14 times as tall.
(c) 2 × 45 = 90 and 3 × 45 = 135. November had 110 mm, which is between them, so November is really only about 2 and a half times as wet as May (110 ÷ 45 = 2.4 to 1 decimal place).
(d) Because the axis starts at 40, the bottom 40 mm of every bar is cut off. This makes May look almost dry and the wet months look huge. A visitor might think May has hardly any rain. The website wants people to come in May, so it makes May look much drier than it really is.
(e) Fair bar chart:
(f) On my fair chart, the November bar is not even 3 times as tall as the May bar. On Chart 3 it looked 14 times as tall. The numbers are the same; only the axis changed.
The pupil finds exactly where the trick is, measures how big it makes the difference look, checks the real difference with the table, and draws a fair chart from 0 with accurate bars. Evidences criterion 4.
| Conclusion | True, false or cannot tell? | Evidence |
|---|---|---|
| (a) Station A is wetter than Station B in every month. | True | I checked all 12 months. Even Station A’s driest month (June, 130 mm) is wetter than Station B’s wettest month (November, 110 mm). |
| (b) It rains every day in Eryri. | Cannot tell | The data only gives a total for each month. A month’s rain could all fall on a few very wet days, so we do not know how many days it rained. |
| (c) At Station B, November is more than 5 times as wet as May. | False | 5 × 45 = 225, but November only had 110 mm. It is about 2.4 times as wet. It only looks like more on Chart 3. |
| (d) Next January, Station A will get exactly 340 mm of rain. | Cannot tell | The data is for one year only. The weather is different every year, so January will probably be wet, but we cannot know the exact amount. |
Every judgement is backed by numbers or by what the data does and does not show. The pupil spots that two conclusions go beyond the data, which is the difference between a wrong conclusion and an uncertain one. Evidences criterion 5.
Dear Morgan family, I advise you to go to Station B’s beach village in Pembrokeshire in May. The data shows that May was the driest month there, with only 45 mm of rain, and April and June were also dry, with 50 mm each. Station A’s valley in Eryri is much wetter: even its driest month, June, had 130 mm, which is more than any month at the beach. Avoid the autumn and winter, because November had 110 mm at the beach and January had 340 mm in the mountains. However, the data cannot tell you what the weather will be like in your week, because it only shows monthly totals for one year, so please still pack a raincoat!
The advice uses exact numbers from the data, compares both places and several months, and says clearly what the data cannot tell the family. Evidences criterion 6.
Spring mean at Station B: 70 + 50 + 45 = 165, and 165 ÷ 3 = 55 mm.
Autumn totals: Station A 220 + 300 + 320 = 840 mm; Station B 75 + 100 + 110 = 285 mm. Autumn minus summer: Station A 840 − 460 = 380 mm, Station B 285 − 170 = 115 mm. Station A has the bigger difference.
Station C: it probably gets less rain than Station A. The wet air drops a lot of its rain as it rises over the mountains, so it is drier by the time it comes down on the far side.