,"latex":"(9.5,4)","labelOrientation":"above"},{"id":"expr-6","color":"green","label":"16–20: height 0.6","latex":"(18,0.6)","labelOrientation":"above"}]}]}],"generatedAt":"2026-07-20T16:49:15.731Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]},{"id":"800eb144-1c8f-46b6-a9ab-a401242b021d","label":"c","content":"One of the participants is selected at random. Estimate the probability that this participant completed the puzzle in under 10 seconds.","markscheme":"- Sums frequencies for under 10s: $2 + 12 + \\frac{3}{4}(8) = 20$ M1\n- Final probability: $\\frac{20}{35}$ A1","marks":2,"order":2,"markingRubric":{"totalMarks":1,"points":[{"id":"p1","marks":1,"description":"Correct probability $\\frac{20}{35}$ or simplified equivalent.","code":"A"}],"finalAnswers":["20/35"],"generatedAt":"2026-05-12T02:14:06.551Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"histogram_probability","label":"Estimate the probability","steps":[{"type":"text","order":0,"title":"Locate the boundary","content":"Because each time is recorded to the nearest second, the class labelled $9$–$10$ has continuous class boundaries $8.5$ and $10.5$. The part below $10$ therefore has width $10-8.5=1.5$, while the whole class has width $10.5-8.5=2$. Hence the estimated proportion below $10$ is\n\n$$\\frac{1.5}{2}=\\frac{3}{4}.$$"},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$n_{<10}=\\htmlData{anchor=calculation}{\\color{@sky}{2+12+\\frac{3}{4}(8)}}$"},{"latex":"$$n_{<10}=\\htmlData{anchor{answer}{\\color{@sky}{20}}}$"}],"highlights":[{"color":"sky","style":"text-color-with-background","anchor":"answer"}],"connections":[{"to":"answer","from":"calculation","color":"sky","label":"evaluate"}]},"order":1,"title":"Count under ten","description":"Multiply the 9–10 class frequency by the proportion below 10 seconds, then add the first two class frequencies. This earns the method mark (M1)."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$P(\\text{under }10)=\\htmlData{anchor=prob_fraction}{\\color{@amber}{\\frac{\\text{estimated frequency under }10}{\\text{total frequency}}}}$"},{"latex":"$$P(\\text{under }10)=\\htmlData{anchor=prob_answer}{\\color{@green}{\\frac{20}{35}}}$"}],"highlights":[{"color":"green","style":"text-color-with-background","anchor":"prob_answer"}],"connections":[{"to":"prob_answer","from":"prob_fraction","color":"green","label":"substitute"}]},"order":2,"title":"Form the probability","description":"Use estimated favourable frequency divided by total frequency. The completed table gives $35$ participants, so this correct probability earns A1."}]}],"generatedAt":"2026-07-20T16:58:35.733Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":73}},{"id":"d29672a6-014c-4db7-9f0e-2c3f4586e5e4","revisionId":"748f1a7b-8534-4cc7-ba84-7f2bfbc285c5","questionNumber":"2","questionType":"LA","specification":"A variable $x$ was measured to the nearest whole number. 50 observations are given in the table below.\n\n| $x$ | 5 – 8 | 9 – 13 | 14 – 20 | 21 – 24 |\n|-----------|-------|--------|---------|---------|\n| Frequency | 10 | 9 | 14 | 17 |\n\nA histogram was drawn and the bar representing the 9 – 13 class has a width of 2 cm and a height of 2.7 cm.","difficulty":1,"difficultyBand":"medium","totalMarks":3,"sourceTitle":"Question Set 3: Representations of Data","calculatorUse":null,"parts":[{"id":"7ab5abc9-4be4-4bc0-8216-6d787f0a64ff","label":"","content":"Find the width and height of the bar representing the 14 – 20 class.","markscheme":"- Width scale factor: $5 \\text{ units} = 2 \\text{ cm} \\times \\frac{5}{2}$ is incorrect, actual class width 9-13 is 5 units. $5 \\text{ units} = 2 \\text{ cm} \\implies 1 \\text{ unit} = 0.4 \\text{ cm}$. M1\n- Width for 14-20 (7 units): $7 \\times 0.4 = 2.8 \\text{ cm}$ (or $\\frac{14}{5}$) A1\n- Height scale factor: Frequency 9, width 2, height 2.7. Area $\\propto$ Freq. $2 \\times 2

Representations of Data

Question 2

Representations of Data Questions

Representations of Data

Question 2

Representations of Data Questions