Worked example · PE · Year 7
DCF: Data and computational thinking → Data and information literacy
A secure Year 7 response, annotated so you can see which success criterion each part meets, and your answer key for the three averages. Show it once pupils have their own figures down.
| Test | Class average (mean) | Lowest | Highest | Range |
|---|---|---|---|---|
| Bleep test level | 7.0 | 5.4 (P07) | 9.3 (P09) | 3.9 |
| Standing long jump (cm) | 171 | 144 (P07) | 205 (P09) | 61 |
| Sit-ups in 60 s | 32 | 22 (P07) | 44 (P09) | 22 |
On the computer I put the codes in column A and the three tests in B, C and D, with the 24 pupils in rows 2 to 25. Then:
=AVERAGE(B2:B25) gave 7 exactly, because the 24 levels add up to 168 and 168 ÷ 24 = 7.
=AVERAGE(C2:C25) gave 171, from a total of 4104 cm ÷ 24.
=AVERAGE(D2:D25) gave 32, from a total of 768 sit-ups ÷ 24.
=MAX(B2:B25)-MIN(B2:B25) gave the range of 3.9 levels.
Correct means, correct ranges, and the totals are shown so the arithmetic can be checked without a computer. Evidences criterion 1.
| Band | Tally | How many pupils | Which pupils |
|---|---|---|---|
| 5.0 to 5.9 | IIII | 4 | P03, P07, P13, P21 |
| 6.0 to 6.9 | IIII III | 8 | P01, P05, P08, P11, P15, P18, P20, P24 |
| 7.0 to 7.9 | IIII II | 7 | P02, P06, P10, P14, P16, P19, P23 |
| 8.0 to 8.9 | IIII | 4 | P04, P12, P17, P22 |
| 9.0 to 9.9 | I | 1 | P09 |
| Total | — | 24 | 4 + 8 + 7 + 4 + 1 = 24, so nobody has been missed or counted twice |
Bands total 24 and the check is written down. On a computer this is =COUNTIFS(B2:B25,">=6",B2:B25,"<7") for the second band. Evidences criterion 2.
Both axes labelled, whole-number scale, a title that says what is being counted and when, and the bar heights match the tally exactly. Evidences criterion 3.
(a) The average bleep test level for the class is exactly 7.0, and 15 of the 24 pupils — just under two thirds — sit in the two middle bands, 6.0 to 6.9 and 7.0 to 7.9. Only one pupil in the whole class reached level 9.
The average standing long jump is 171 cm, and the class is spread over 61 cm, from 144 cm to 205 cm. That is a bigger gap than most people would guess from watching a PE lesson.
Two conclusions, each carrying a figure from the table rather than a general impression. Evidences criterion 4.
(b) The sit-ups have the widest spread once you compare each range with its own average. The sit-up range of 22 is about 69% of the average of 32; the bleep test range of 3.9 is about 56% of 7.0; the long jump range of 61 cm is only about 36% of 171 cm. Sit-ups depend a lot on technique and on how hard you are willing to push in the last 15 seconds, so I would expect it to vary more between pupils than a single explosive jump does.
Compares spread fairly by relating each range to its own average instead of comparing 61 with 3.9. Evidences criteria 1 and 4.
(c) It cannot tell us whether anyone is getting fitter, because it is one test day. To show improvement you would need the same 24 pupils tested again later and compared with themselves. It also cannot tell us why P07 scored lowest — they might have been ill, or new to the test, or pacing themselves badly on the bleeps.
(d) Codes are used because a fitness score is personal information. A class list of who is slowest is exactly the sort of thing that gets used to tease people, and it would put pupils off trying. With codes, the class can still work out its own average and spread, which is all this task needs, and nobody's name is attached to a number on a sheet that gets passed around.
States a genuine limit of the data set and gives a real safeguarding reason for anonymising it. Evidences criterion 5.