Worked example · Geography · Year 8
LNF: Numeracy → Learning that statistics represent data and that probability models chance helps us make informed inferences and decisions → Interpreting data
A secure Year 8 response, annotated to show which success criterion each part meets. It is also your answer key. Medians from west to east: 90, 74, 59, 46.5 and 36 mm. Ranges: 48, 28, 161, 13 and 11 mm. The outlier is the 210 mm rock at site 3. Without it, site 3 has a mean of 57.8 mm and a range of 15 mm. The key idea: pebbles get smaller and more similar in size from west to east, which supports longshore drift and attrition.
| Site | Values in order (mm) |
|---|---|
| Site 1 | 72, 78, 85, 85, 88, 92, 96, 104, 110, 120 |
| Site 3 | 49, 52, 55, 57, 58, 60, 61, 64, 64, 210 |
| Site 5 | 29, 31, 33, 34, 36, 36, 36, 37, 38, 40 |
Site 2 in order: 62, 66, 70, 71, 74, 74, 78, 80, 85, 90. Site 4 in order: 39, 41, 44, 44, 46, 47, 48, 49, 50, 52.
Each list has exactly 10 values, so none were missed. Evidences criterion 1.
| Site | Total (mm) | Mean (mm) | Median (mm) | Mode (mm) | Range (mm) |
|---|---|---|---|---|---|
| Site 1 | 930 | 930 ÷ 10 = 93.0 | (88 + 92) ÷ 2 = 90 | 85 | 120 − 72 = 48 |
| Site 2 | 750 | 75.0 | (74 + 74) ÷ 2 = 74 | 74 | 28 |
| Site 3 | 730 | 730 ÷ 10 = 73.0 | (58 + 60) ÷ 2 = 59 | 64 | 210 − 49 = 161 |
| Site 4 | 460 | 46.0 | (46 + 47) ÷ 2 = 46.5 | 44 | 13 |
| Site 5 | 350 | 350 ÷ 10 = 35.0 | (36 + 36) ÷ 2 = 36 | 36 | 40 − 29 = 11 |
Working is shown. With 10 values, the median is halfway between the 5th and 6th values. Evidences criterion 1.
Bars are drawn with a ruler to the correct height on a scale of 0 to 100 mm, with values, a title and labelled axes. The steady fall from left to right is easy to see. Evidences criterion 2.
(a) Pebble 5, 210 mm. It is a lump of rock from the old sea wall, not a beach pebble, and it is more than 3 times the size of any other pebble at site 3.
(b) Without it: total 730 − 210 = 520; mean 520 ÷ 9 = 57.8 mm. Range 64 − 49 = 15 mm. The mean fell by 15.2 mm and the range fell from 161 mm to 15 mm.
(c) The median (59 mm) is best, because it is not pulled up by the 210 mm rock the way the mean (73.0 mm) is, and it is close to the mean without the outlier.
The pupil shows how one extreme value changes the mean and the range but hardly changes the median, then uses that to choose an average. Evidences criteria 3 and 4.
(a) From west to east, the median pebble size falls from 90 mm at site 1 to 36 mm at site 5. The range falls from 48 mm to 11 mm, which means the pebbles at the east end are much more similar in size.
(b) Yes. The median gets smaller at every site as you move east, by 54 mm in total over 800 metres. This fits the idea that pebbles are carried east by longshore drift and worn down by attrition on the way. The smaller range at the east end also fits, because pebbles that have travelled further have been worn down to a similar size.
(c) First, only 10 pebbles were measured at each site, which is a small sample. Second, pupils may have measured the long axis differently, or chosen a pebble near the tape rather than the one touching it. The survey was also done on one day only.
The conclusion quotes figures for both the average and the spread, links the pattern to the geography, and says why the result is uncertain. Evidences criterion 5.