sourceTitle":"Averages","calculatorUse":"non_calc","parts":[{"id":"c086e594-f5d3-48c6-b7ea-9492fd75aa02","label":"a","content":"Work out the range of the numbers on the cards.","markscheme":"- $18 - 5 = 13$ B1","marks":1,"order":0,"markingRubric":{"totalMarks":1,"points":[{"id":"p1","marks":1,"description":"Calculates the range as $18 - 5 = 13$.","code":"B"}],"finalAnswers":["13"],"generatedAt":"2026-05-06T01:43:28.888Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"largest_minus_smallest","label":"Largest minus smallest","steps":[{"type":"text","order":0,"title":"Identify the extremes","content":"The **range** measures the spread from the smallest number to the largest number. Here, the smallest number is $5$ and the largest number is $18$.","highlights":[{"text":"range of the numbers","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\mathrm{Range}=\\color{@sky}{\\htmlData{anchor=largest}{18}}-\\color{@amber}{\\htmlData{anchor=smallest}{5}}$"},{"latex":"$$\\mathrm{Range}=\\color{@green}{\\htmlData{anchor=result}{13}}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"largest"},{"color":"amber","style":"text-color","anchor":"smallest"},{"color":"green","style":"text-color","anchor":"result"}],"connections":[{"to":"result","from":"largest","color":"sky","label":"subtract 5","style":"solid"}]},"order":1,"title":"Subtract the extremes","description":"Use range = largest value − smallest value. Writing 18 − 5 = 13 earns the B1 mark."}]}],"generatedAt":"2026-07-20T11:00:59.269Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]},{"id":"595dd3e7-eb99-48b2-b45a-dad1f08ca127","label":"b","content":"Work out the median of the numbers on the cards.","markscheme":"- Order numbers: 5, 9, 10, 11, 12, 12, 18 M1\n- Median is 11 A1","marks":2,"order":1,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Orders the numbers to find the middle value.","code":"M"},{"id":"p2","marks":1,"description":"Identifies the middle number as 11.","code":"A"}],"finalAnswers":["11"],"generatedAt":"2026-05-06T01:43:28.888Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"order_then_middle","label":"Order then find the middle","steps":[{"type":"text","order":0,"title":"Order the numbers","content":"Put the numbers in ascending order, which means from smallest to largest:\n\n$$5,\\ 9,\\ 10,\\ 11,\\ 12,\\ 12,\\ 18$$\n\nWriting the complete ordered list earns **M1**. Remember to include both cards showing $12$.","highlights":[{"text":"Here are seven cards. Each card has a number on it.","location":"specification"}]},{"type":"text","order":1,"title":"Choose the middle value","content":"There are seven ordered values, so the median is the fourth value: $11$. Therefore, the median is $11$. This correct value earns **A1**.","highlights":[{"text":"median","location":"specification"}]}]}],"generatedAt":"2026-07-20T11:03:39.288Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]},{"id":"c98c9c6b-f5a2-4fe3-af85-e3b231c059a8","label":"c","content":"Work out the mean of the numbers on the cards.","markscheme":"- Sum of numbers: $5 + 9 + 10 + 11 + 12 + 12 + 18 = 77$ M1\n- Mean: $77 \\div 7 = 11$ A1","marks":2,"order":2,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Calculates the sum of the 7 numbers (77).","code":"M"},{"id":"p2","marks":1,"description":"Divides the sum by 7 to get 11.","code":"A"}],"finalAnswers":["11"],"generatedAt":"2026-05-06T01:43:28.888Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"add_then_divide","label":"Add then divide","steps":[{"type":"text","order":0,"title":"Recall the mean","content":"To find the **mean**, add all the numbers, then divide by how many numbers there are. There are $7$ cards, so the total will be divided by $7$.","highlights":[{"text":"mean of the numbers on the cards","location":"specification"}]},{"type":"hyper_latex","blo

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