Worked example · Art · Year 9
DCF: Data and computational thinking → Data and information literacy
Also assessed, LNF: Numeracy → Statistics and probability → Representing data
A secure Year 9 response, annotated against the success criteria. Repeats: 10, 11, 21 and 24, leaving 36. Stars 1 to 5: 2, 3, 7, 13, 11. Found us by: school website 8, social media 12, email newsletter 6, search engine 3, word of mouth 7. Pie angles: 80°, 120°, 60°, 30°, 70°. Mean 3.8, median 4, mode 4, range 4. Accept drawn bars and angles within 2° or half a square.
The numeracy (Representing data) evidence is the bar chart in Step 3, the pie chart and its angle working in Step 4 and the fair redraw in Step 5(c). The data literacy evidence is Steps 1, 5 and 6.
(a) Repeats: 10, 11, 21, 24. 40 − 4 = 36 genuine responses. All 4 repeats are 5 stars, social media, phone.
(b) They were sent at different times (1 March 12:07 and 5 March 22:44), so they are almost certainly 2 different visitors who happened to give the same answers.
Applies the rule exactly: same minute and same answers, not just same answers. Evidences criterion 1.
| Stars | 1 | 2 | 3 | 4 | 5 | Total |
|---|---|---|---|---|---|---|
| Frequency | 2 | 3 | 7 | 13 | 11 | 36 |
| Found us by | Freq. | Device | Freq. |
|---|---|---|---|
| School website | 8 | Phone | 18 |
| Social media | 12 | Tablet | 5 |
| Email newsletter | 6 | Laptop | 9 |
| Search engine | 3 | Desktop computer | 4 |
| Word of mouth | 7 | Total | 36 |
| Total | 36 |
Tallies grouped in fives and every table totals 36, which proves no row was missed or counted twice. Evidences criterion 2.
Bar chart: title “Star ratings for Tirlun (36 genuine responses)”. Horizontal axis “Stars” with bars for 1, 2, 3, 4, 5; vertical axis “Number of visitors” from 0 to 14, 1 square = 1 visitor. Bar heights 2, 3, 7, 13, 11, all 2 squares wide with 1-square gaps, because star ratings are separate categories.
Mean: (1 × 2) + (2 × 3) + (3 × 7) + (4 × 13) + (5 × 11) = 2 + 6 + 21 + 52 + 55 = 136; 136 ÷ 36 = 3.777… = 3.8 stars.
Median: halfway between the 18th and 19th values. Running totals: 2, 5, 12, 25, so values 13 to 25 are all 4. Median = 4 stars.
Mode: 4 stars (13 visitors). Range: 5 − 1 = 4.
The median and mode, 4 stars, sum up the ratings best: the 2 one-star ratings pull the mean down below what most visitors gave.
Accurate chart with a scale from 0 and gaps between bars; every average shown with working and the choice of average justified. Evidences criteria 3 and 5, and the numeracy element.
360 ÷ 36 = 10° per visitor. School website 8 × 10 = 80° · social media 12 × 10 = 120° · email newsletter 6 × 10 = 60° · search engine 3 × 10 = 30° · word of mouth 7 × 10 = 70°. Check: 80 + 120 + 60 + 30 + 70 = 360°.
Title: “How 36 visitors found Tirlun”.
Working shown for every angle, the total checked, sectors measured from each new line and a key added. Evidences criterion 4 and the numeracy element.
(a) The axis starts at 5, so the social media bar shows 16 − 5 = 11 units and the school website bar 8 − 5 = 3 units. It looks 11 ÷ 3 = 3.7 times taller. The real numbers are 16 ÷ 8 = 2 times, and with the repeats removed only 12 ÷ 8 = 1.5 times.
(b) The search engine bar has vanished, because 3 is below where the axis starts. The chart counts the 4 repeats, which were all social media, so social media is 16 instead of 12. The vertical axis has no label. “Most of you” is false: 12 out of 36 is one third, so two thirds found the exhibition another way. “40 visitors” should be 36, and the genuine mean is 3.8, not 3.9.
(c) Fair chart: title “How 36 visitors found Tirlun”, vertical axis “Number of visitors” from 0 to 12 (or 14), bars 8, 12, 6, 3, 7, every bar visible.
Quantifies the distortion instead of just saying “it starts at 5”, links the chart to the dirty data, and redraws it correctly. Evidences criteria 3 and 6, and the numeracy element.
(a) 36 ÷ 450 × 100 = 8% of visits.
(b) This is a self-selected sample. Visitors who gave up before the last page never saw the form, including people who could not view the pictures on a phone. People who loved it, such as pupils’ families, are more likely to bother. So the real ratings are probably lower than these.
(c) “How would you rate the exhibition? 1 star = poor, 5 stars = excellent.”
(d) Q2 has no “Other” option, so people who found it another way had to pick a wrong answer; add “Other”. Fix the repeats by blocking a second submission. With the repeats left in, 5 stars has 11 + 4 = 15 and 4 stars has 13, so the mode becomes 5: just 4 repeats changed the headline answer.
Separates who answered from who visited, rewrites the question neutrally and shows with a number how dirty data changes a result. Evidences criteria 1 and 6.
Social media was the biggest single way in, 12 of 36 visitors (120°, a third of the pie), so keep using it, but it is not “most”: two thirds came another way. The school website (8 visitors, 80°) and word of mouth (7, 70°) together brought more people than social media, so the gallery should advertise on social media and the school website, and keep the newsletter. Only 3 visitors (30°) came from a search engine, so the page needs a clearer title that people can find. Half the visitors (18 of 36) used a phone, 4 of the 5 who gave 1 or 2 stars were on a phone, and 2 of them said the pictures were tiny or would not zoom, so the pictures must be easy to enlarge on a phone.
Every claim is backed by a frequency or angle, the post’s claim is corrected, and the device data leads to a practical change. Evidences criterion 7.