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125 133 144 105","difficulty":1,"difficultyBand":"easy","totalMarks":3,"sourceTitle":"Averages","calculatorUse":null,"isCalculation":true,"parts":[{"id":"3e556d6c-afa3-43a3-8e62-1ad0bb967926","label":"a","content":"Work out the range.","markscheme":"- $150 - 105 = 45$ B1","marks":1,"order":0,"markingRubric":{"totalMarks":1,"points":[{"id":"p1","marks":1,"description":"Correct range of 45.","code":"B"}],"finalAnswers":["45"],"generatedAt":"2026-05-06T15:36:46.080Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"subtract_extremes","label":"Subtract the smallest from largest","steps":[{"type":"text","order":0,"title":"Find the extremes","content":"The **range** is the largest value minus the smallest value. 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This complete calculation earns the B1 mark."}]}],"generatedAt":"2026-07-20T16:55:03.751Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]},{"id":"ad5b14cf-9cb2-4742-95ad-a627f69123b1","label":"b","content":"Work out the median weight.","markscheme":"- Ordered list: 105, 125, 129, 133, 144, 150 M1\n- Median is $\\frac{129 + 133}{2} = 131$ A1","marks":2,"order":1,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Orders the list and identifies the middle two numbers.","code":"M"},{"id":"p2","marks":1,"description":"Final answer of 131.","code":"A"}],"finalAnswers":["131"],"generatedAt":"2026-05-06T15:36:46.080Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"order_then_middle","label":"Order then find the middle","steps":[{"type":"text","order":0,"title":"Order the weights","content":"Write the weights in ascending order (smallest to largest):\n\n$$105,\\ 125,\\ 129,\\ 133,\\ 144,\\ 150$$\n\nThis ordered list earns the **M1** mark. Ordering is essential because the median is the middle value.","highlights":[{"text":"Work out the median weight.","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\text{middle weights}=\\htmlData{anchor=pair}{\\color{@sky}{129\\text{ and }133}}"},{"latex":"\\text{median}=\\htmlData{anchor=average}{\\color{@green}{\\frac{129+133}{2}}}"},{"latex":"\\text{median}=\\htmlData{anchor=answer}{\\color{@green}{131\\text{ g}}}"}],"highlights":[{"color":"green","style":"text-color-with-background","anchor":"average"}],"connections":[{"to":"average","from":"pair","color":"sky","label":"average them"},{"to":"answer","from":"average","color":"green","label":"calculate"}]},"order":1,"title":"Average the middle pair","description":"There are six values, so there is no single middle value. Average the two middle weights, 129 and 133. Averaging the two middle values to get 131 earns the A1 mark."}]}],"generatedAt":"2026-07-21T03:56:09.955Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":57},"walkthroughVideo":null},{"id":"51f71461-f25a-4b84-8942-61b2b536748c","revisionId":"4cad1610-744e-458b-8998-d82d662ac2ce","questionNumber":"5","questionType":"LA","specification":"Here are six cards. Each card has a number on it.\n\n| 19 | 7 | 11 | 8 | 15 | 15 |","difficulty":1,"difficultyBand":"easy","totalMarks":3,"sourceTitle":"Averages","calculatorUse":null,"isCalculation":true,"parts":[{"id":"f29ed3ed-4796-4632-b539-fc49c38ddc1f","label":"a","content":"Work out the range of the numbers on the cards.","markscheme":"- $19 - 7 = 12$ B1","marks":1,"order":0,"markingRubric":{"totalMarks":1,"points":[{"id":"p1","marks":1,"description":"Correct range of 12.","code":"B"}],"finalAnswers":["12"],"generatedAt":"2026-05-06T15:36:46.080Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"largest_minus_smallest","label":"Largest minus smallest","steps":[{"type":"text","order":0,"title":"Find the extremes","content":"The **range** is the difference between the largest and smallest values. From the cards, the largest number is $19$ and the smallest number is $7$.","highlights":[{"text":"| 19 | 7 | 11 | 8 | 15 | 15 |","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\text{range}=\\htmlData{anchor=calculation}{\\color{@sky}{19-7}}"},{"latex":"\\text{range}=\\htmlData{anchor=answer}{\\color{@green}{12}}"}],"highlights":[{"color":"sky","style":"text-color-with-background","anchor":"calculation"},{"color":"green","style":"text-color-with-background","anchor":"answer"}],"connections":[{"to":"answer","from":"calculation","color":"sky","label":"subtract"}]},"order":1,"title":"Subtract the values","description":"Subtract the smallest value from the largest value. This gives the range and earns the mark."}]}],"generatedAt":"2026-07-21T03:54:48.642Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]},{"id":"198581bb-a2ca-4d87-9e92-a2e1e3f6dbe3","label":"b","content":"Work out the mean of the numbers on the cards.","markscheme":"- Sum: $19 + 11 + 15 + 15 + 8 + 7 = 75$ M1\n- $75 \\div 6 = 12.5$ A1","marks":2,"order":1,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Shows sum of 75 or division by 6.","code":"M"},{"id":"p2","marks":1,"description":"Final answer of 12.5.","code":"A"}],"finalAnswers":["12.5"],"generatedAt":"2026-05-06T15:36:46.080Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"mean_method","label":"Add then divide","steps":[{"type":"text","order":0,"title":"Use the mean rule","content":"The **mean** is found by adding all the values, then dividing by how many values there are. There are six cards, so we need the total divided by $6$.","highlights":[{"text":"Work out the mean of the numbers on the cards.","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\text{total}=\\htmlData{anchor=sum}{\\color{@amber}{19+11+15+15+8+7}}$"},{"latex":"$$\\text{total}=\\htmlData{anchor=total75}{\\color{@sky}{75}}$"}],"highlights":[{"color":"amber","style":"text-color","anchor":"sum"},{"color":"sky","style":"text-color","anchor":"total75"}],"connections":[{"to":"total75","from":"sum","color":"sky","label":"add"}]},"order":1,"title":"Add the card values","description":"Add each number once. This earns the M1 mark for finding the correct total."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\text{mean}=\\htmlData{anchor=fraction}{\\color{@amber}{\\frac{75}{6}}}$"},{"latex":"$$\\text{mean}=\\htmlData{anchor=answer}{\\color{@green}{12.5}}$"}],"highlights":[{"color":"green","style":"text-color-with-background","anchor":"answer"}],"connections":[{"to":"answer","from":"fraction","color":"green","label":"divide"}]},"order":2,"title":"Divide by six","description":"Divide the total by the number of cards. This earns the A1 mark."}]}],"generatedAt":"2026-07-21T03:56:17.704Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":90},"walkthroughVideo":null},{"id":"d39afe65-8980-4f72-81a6-e2a671725e6d","revisionId":"bf6e52cf-fe2c-4d1b-b52a-54bdacf1d987","questionNumber":"6","questionType":"LA","specification":"Here is a list of 10 numbers.\n\n1 4 4 5 6 8 11 11 11 14","difficulty":1,"difficultyBand":"easy","totalMarks":2,"sourceTitle":"Averages","calculatorUse":null,"isCalculation":true,"parts":[{"id":"662d0f6a-4498-400d-9832-b3cbe6bd197e","label":"a","content":"Work out the range.","markscheme":"- $14 - 1 = 13$ B1","marks":1,"order":0,"markingRubric":{"totalMarks":1,"points":[{"id":"p1","marks":1,"description":"Correct range of 13.","code":"B"}],"finalAnswers":["13"],"generatedAt":"2026-05-06T15:36:46.080Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"largest-minus-smallest","label":"Largest minus smallest","steps":[{"type":"text","order":0,"title":"Find the end values","content":"The **range** tells you how spread out the data are. It is found by subtracting the smallest number from the largest number.\n\nThe list is already in order, so the smallest value is $1$ and the largest value is $14$.","highlights":[{"text":"1 4 4 5 6 8 11 11 11 14","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\text{range}=\\htmlData{anchor=largest}{14}-1"},{"latex":"\\text{range}=\\htmlData{anchor=answer}{13}"}],"connections":[{"to":"answer","from":"largest","color":"sky","label":"subtract 1"}]},"order":1,"title":"Subtract for the range","description":"Always use largest minus smallest, in that order. This calculation earns the one mark."}]}],"generatedAt":"2026-09-01T09:03:36.508Z","modelVersion":"gpt-5.6-terra+diagrams-2","explanationVersion":"v3"},"options":[]},{"id":"18f5916a-da6c-433e-8d98-6337625cbe0f","label":"b","content":"Find the mode.","markscheme":"- Mode is 11 B1","marks":1,"order":1,"markingRubric":{"totalMarks":1,"points":[{"id":"p1","marks":1,"description":"Correct mode of 11.","code":"B"}],"finalAnswers":["11"],"generatedAt":"2026-05-06T15:36:46.080Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"count_frequencies","label":"Count frequencies","steps":[{"type":"text","order":1,"title":"Count each number","content":"The **mode** is the number that occurs most often. Counting the list: $1,5,6,8,$ and $14$ occur once; $4$ occurs twice; and $11$ occurs three times.\n\nSo $11$ has the greatest frequency.","highlights":[{"text":"Find the mode.","location":"specification"}]},{"type":"text","order":2,"title":"State the mode","content":"Since $11$ has the greatest frequency, the mode is\n\n$$11$$\n\nThis earns the $1$ mark.","highlights":[{"text":"Find the mode.","location":"specification"}]}]}],"generatedAt":"2026-07-21T04:04:25.125Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":{"methods":[{"id":"662d0f6a-4498-400d-9832-b3cbe6bd197e:largest-minus-smallest","label":"(a) Largest minus smallest","steps":[{"type":"text","order":0,"title":"Find the end values","content":"The **range** tells you how spread out the data are. It is found by subtracting the smallest number from the largest number.\n\nThe list is already in order, so the smallest value is $1$ and the largest value is $14$.","highlights":[{"text":"1 4 4 5 6 8 11 11 11 14","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"\\text{range}=\\htmlData{anchor=largest}{14}-1"},{"latex":"\\text{range}=\\htmlData{anchor=answer}{13}"}],"connections":[{"to":"answer","from":"largest","color":"sky","label":"subtract 1"}]},"order":1,"title":"Subtract for the range","description":"Always use largest minus smallest, in that order. This calculation earns the one mark."}]},{"id":"18f5916a-da6c-433e-8d98-6337625cbe0f:count_frequencies","label":"(b) Count frequencies","steps":[{"type":"text","order":1,"title":"Count each number","content":"The **mode** is the number that occurs most often. Counting the list: $1,5,6,8,$ and $14$ occur once; $4$ occurs twice; and $11$ occurs three times.\n\nSo $11$ has the greatest frequency.","highlights":[{"text":"Find the mode.","location":"specification"}]},{"type":"text","order":2,"title":"State the mode","content":"Since $11$ has the greatest frequency, the mode is\n\n$$11$$\n\nThis earns the $1$ mark.","highlights":[{"text":"Find the mode.","location":"specification"}]}]}],"generatedAt":"2026-09-01T09:03:36.815Z","modelVersion":"gpt-5.6-terra+diagrams-2","explanationVersion":"v3"},"firstAttemptFullMarks":null,"walkthroughVideo":null}],"subjectCode":"igcse_maths__oxford_aqa","summaries":[{"id":"fb42bec9-c187-4405-8685-189346e44ad8","difficultyBand":"easy","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"a9395a80-544a-4001-9239-a9b566bb93d6","difficultyBand":"easy","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"185b8ab9-2b50-4391-ac86-231fc4ed177a","difficultyBand":"easy","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"1bbdea9a-ef63-45be-bf4b-ee24f5f8257f","difficultyBand":"easy","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"51f71461-f25a-4b84-8942-61b2b536748c","difficultyBand":"easy","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"d39afe65-8980-4f72-81a6-e2a671725e6d","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"5797ecea-9f1a-4537-afe2-d92ec2737923","difficultyBand":"easy","calculatorUse":null,"totalMarks":5,"questionType":"LA","isCalculation":true},{"id":"186e22ec-be43-43f3-8abf-e77148c0df58","difficultyBand":"medium","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"684affba-5c65-40a7-84f5-20cb9bf1eae1","difficultyBand":"easy","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"163a639e-cbc4-4739-8228-ca32ad5dd1d0","difficultyBand":"easy","calculatorUse":null,"totalMarks":2,"questionType":"LA","isCalculation":true},{"id":"61e02b0a-58d0-4cbb-9989-cbb6f1dde9f0","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"fe426d45-33bf-4d51-b49c-31d49611a0da","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true}],"title":"Averages","topicId":"07bf142c-a8cf-49e9-9898-15b7333c1339","topicSidebar":"$L3b","topicSlug":"grade-2-2-14-averages","topicTitle":"Averages"}]}],"$L3c","$L3d"]}]