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171 167 188 190 151","difficulty":1,"difficultyBand":"easy","totalMarks":4,"sourceTitle":"Averages","calculatorUse":null,"isCalculation":true,"parts":[{"id":"f19a94a5-465b-4a7b-af7e-828dd70f9e3f","label":"a","content":"Work out the range.","markscheme":"- $190 - 151 = 39$ B1","marks":1,"order":0,"markingRubric":{"totalMarks":1,"points":[{"id":"p1","marks":1,"description":"Correct range of 39.","code":"B"}],"finalAnswers":["39"],"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":"Recall the range","content":"The **range** is the largest value minus the smallest value.","highlights":[{"text":"Work out the range.","location":"specification"}]},{"type":"text","order":1,"title":"Find the extremes","content":"From the list, the smallest height is $151\\text{ cm}$ and the largest height is $190\\text{ cm}$. Repeated values do not affect the range.","highlights":[{"text":"155 171 164 171 167 188 190 151","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\text{range}=\\htmlData{anchor=extremes}{\\color{@sky}{190-151}}$"},{"latex":"$$\\text{range}=\\htmlData{anchor=answer}{\\color{@green}{39\\text{ cm}}}$"}],"highlights":[{"color":"green","style":"text-color-with-background","anchor":"answer"}],"connections":[{"to":"answer","from":"extremes","color":"green","label":"subtract"}]},"order":2,"title":"Subtract the extremes","description":"Subtract the smallest height from the largest height. This complete calculation earns the B1 mark."}]}],"generatedAt":"2026-07-20T16:38:36.374Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]},{"id":"c1560ecc-0689-49eb-a8fa-2941751ddeb5","label":"b","content":"Find the mode.","markscheme":"- Mode is 171 B1","marks":1,"order":1,"markingRubric":{"totalMarks":1,"points":[{"id":"p1","marks":1,"description":"Correct mode of 171.","code":"B"}],"finalAnswers":["171"],"generatedAt":"2026-05-06T15:36:46.080Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"find_mode","label":"Find the mode","steps":[{"type":"text","order":0,"title":"Count repeats","content":"The mode is the value that appears most often. In the list, $171$ appears twice; every other height appears once. Therefore, the mode is $171$. This earns the B1 mark.","highlights":[{"text":"155 171 164 171 167 188 190 151","location":"specification"}]}]}],"generatedAt":"2026-07-20T16:40:56.559Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]},{"id":"fa39c9c2-381b-48e9-9661-b306324b4e30","label":"c","content":"Calculate the mean.","markscheme":"- Sum of heights: $155 + 171 + 164 + 171 + 167 + 188 + 190 + 151 = 1357$ M1\n- $1357 \\div 8 = 169.625$ A1","marks":2,"order":2,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Shows sum of 1357 or division by 8.","code":"M"},{"id":"p2","marks":1,"description":"Final answer of 169.625.","code":"A"}],"finalAnswers":["169.625"],"generatedAt":"2026-05-06T15:36:46.080Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"sum_then_divide","label":"Add then divide","steps":[{"type":"text","order":0,"title":"Recall the mean","content":"To calculate the mean, add all the heights, then divide the total by the number of people. There are $8$ heights, so the divisor will be $8$.","highlights":[{"text":"Calculate the mean.","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\htmlData{anchor=sum}{\\color{@sky}{155+171+164+171+167+188+190+151}}$"},{"latex":"$$\\htmlData{anchor=total}{\\color{@sky}{\\text{total}=1357\\text{ cm}}}$"}],"highlights":[{"color":"sky","anchor":"sum"},{"color":"sky","style":"text-color-with-background","anchor":"total"}],"connections":[{"to":"total","from":"sum","color":"sky","label":"add"}]},"order":1,"title":"Add the heights","description":"Adding every height gives the total. Showing this complete addition earns the M1 method mark."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\text{mean}=\\htmlData{anchor=division}{\\color{@amber}{1357\\div 8}}$"},{"latex":"$$\\htmlData{anchor=answer}{\\color{@green}{\\text{mean}=169.625\\text{ cm}}}$"}],"highlights":[{"color":"amber","anchor":"division"},{"color":"green","style":"text-color-with-background","anchor":"answer"}],"connections":[{"to":"answer","from":"division","color":"green","label":"calculate"}]},"order":2,"title":"Divide by eight","description":"Divide the total by the number of people. This correct calculation earns the A1 accuracy mark."}]}],"generatedAt":"2026-07-20T16:42:15.995Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":61},"walkthroughVideo":null},{"id":"1bbdea9a-ef63-45be-bf4b-ee24f5f8257f","revisionId":"c1c627e1-37f0-4f7f-bf90-9ce62559b602","questionNumber":"4","questionType":"LA","specification":"Here are the weights, in grams, of 6 potatoes\n\n150 129 125 133 144 105","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. Here, the largest weight is $150$ g and the smallest weight is $105$ g.","highlights":[{"text":"150 129 125 133 144 105","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\mathrm{Range}=\\htmlData{anchor=subtraction}{\\color{@sky}{150-105}}$"},{"latex":"$$\\mathrm{Range}=\\htmlData{anchor=result}{\\color{@green}{45\\text{ g}}}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"subtraction"},{"color":"green","style":"text-color-with-background","anchor":"result"}],"connections":[{"to":"result","from":"subtraction","color":"sky","label":"calculate"}]},"order":1,"title":"Subtract the weights","description":"Subtract the smallest weight from the largest. 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}],"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"]}]