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This calculation earns the mark."}]}],"generatedAt":"2026-07-21T03:52:02.384Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]},{"id":"73ef16c2-d7bf-470f-8a56-9215466573f2","label":"b","content":"Find the mode.","markscheme":"- Mode is 4 B1","marks":1,"order":1,"markingRubric":{"totalMarks":1,"points":[{"id":"p1","marks":1,"description":"Correct mode of 4.","code":"B"}],"finalAnswers":["4"],"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":"Identify the mode","content":"The **mode** is the value that occurs most often. In the list, $4$ appears $3$ times, while every other number appears fewer times.\n\nTherefore, $$\\boxed{4}$$\n\nThis is the required answer for the B1 mark.","highlights":[{"text":"Find the mode.","location":"specification"}]}]}],"generatedAt":"2026-07-21T03:52:39.528Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]},{"id":"82422ec5-db34-4539-88b0-f1f56b596269","label":"c","content":"Calculate the mean.","markscheme":"- Sum of numbers: $2 + 3 + 4 + 4 + 4 + 5 + 6 + 6 + 7 + 7 = 48$ M1\n- $48 \\div 10 = 4.8$ A1","marks":2,"order":2,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Shows sum of 48 or division by 10.","code":"M"},{"id":"p2","marks":1,"description":"Final answer of 4.8.","code":"A"}],"finalAnswers":["4.8"],"generatedAt":"2026-05-06T15:36:46.080Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"sum_then_divide","label":"Sum then divide","steps":[{"type":"text","order":0,"title":"Use the mean rule","content":"The **mean** is the total of all the values divided by how many values there are. There are $10$ numbers in the list, so first find their total.","highlights":[{"text":"Here is a list of 10 numbers.","location":"specification"},{"text":"Calculate the mean.","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"2+3+4+4+4+5+6+6+7+7=\\htmlData{anchor=total}{\\color{@sky}{48}}"},{"text":"Use this total in the next calculation."}],"highlights":[{"color":"sky","style":"text-color-with-background","anchor":"total"}]},"order":1,"title":"Add every value","description":"Add all ten numbers once. This total earns the first mark."},{"type":"hyper_latex","block":{"nodes":[{"text":"There are 10 values in the list."},{"latex":"48\\div 10=\\htmlData{anchor=mean}{\\color{@green}{4.8}}"}],"highlights":[{"color":"green","style":"text-color-with-background","anchor":"mean"}]},"order":2,"title":"Divide by ten","description":"Now divide the total by the number of values. This earns the accuracy mark."}]}],"generatedAt":"2026-07-21T03:58:19.800Z","modelVersion":"gpt-5.6-terra","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":43},"walkthroughVideo":null},{"id":"a9395a80-544a-4001-9239-a9b566bb93d6","revisionId":"1c6a0452-6fb9-44f7-92b5-abc708722177","questionNumber":"2","questionType":"LA","specification":"Here is a list of 5 numbers.\n\n4 6 9 10 11","difficulty":1,"difficultyBand":"easy","totalMarks":4,"sourceTitle":"Averages","calculatorUse":null,"isCalculation":true,"parts":[{"id":"5cae2e70-3503-45a2-a688-64b2016bf232","label":"a","content":"Work out the range.","markscheme":"- $11 - 4 = 7$ B1","marks":1,"order":0,"markingRubric":{"totalMarks":1,"points":[{"id":"p1","marks":1,"description":"Correct range of 7.","code":"B"}],"finalAnswers":["7"],"generatedAt":"2026-05-06T15:36:46.080Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"range","label":"Find the range","steps":[{"type":"text","order":0,"title":"Identify the extremes","content":"The **range** is the difference between the largest and smallest values. Here, the smallest value is $4$ and the largest value is $11$.","highlights":[{"text":"4 6 9 10 11","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\mathrm{Range}=\\htmlData{anchor=calculation}{\\color{@sky}{11-4}}$"},{"latex":"$$\\mathrm{Range}=\\htmlData{anchor=answer}{\\color{@green}{7}}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"calculation"},{"color":"green","style":"text-color-with-background","anchor":"answer"}],"connections":[{"to":"answer","from":"calculation","color":"sky","label":"calculate"}]},"order":1,"title":"Subtract the smallest","description":"Subtract the smallest value from the largest value. This complete calculation earns the B1 mark."}]}],"generatedAt":"2026-07-20T16:24:43.291Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]},{"id":"33b89caa-5b86-4b98-94e5-95c7d34fe24b","label":"b","content":"Write down the median.","markscheme":"- Median is 9 B1","marks":1,"order":1,"markingRubric":{"totalMarks":1,"points":[{"id":"p1","marks":1,"description":"Correct median of 9.","code":"B"}],"finalAnswers":["9"],"generatedAt":"2026-05-06T15:36:46.080Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"find_median","label":"Find the median","steps":[{"type":"text","order":0,"title":"Check the order","content":"The numbers are already in ascending order, from smallest to largest. The median is the middle number in an ordered list.","highlights":[{"text":"4 6 9 10 11","location":"specification"}]},{"type":"text","order":1,"title":"Choose the middle","content":"There are $5$ numbers, so the third number is the middle one: $4,\\ 6,\\ \\boxed{9},\\ 10,\\ 11$. Writing $9$ earns the B1 mark.","highlights":[{"text":"Write down the median.","location":"specification"}]}]}],"generatedAt":"2026-07-20T16:25:26.428Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]},{"id":"a4c30fa1-06a6-4d3c-91ae-aae6b1edf28a","label":"c","content":"Calculate the mean.","markscheme":"- Sum of numbers: $4 + 6 + 9 + 10 + 11 = 40$ M1\n- $40 \\div 5 = 8$ A1","marks":2,"order":2,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Shows sum of 40 or division by 5.","code":"M"},{"id":"p2","marks":1,"description":"Final answer of 8.","code":"A"}],"finalAnswers":["8"],"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 numbers and then divide by how many numbers there are. The list contains $5$ numbers.","highlights":[{"text":"Calculate the mean.","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\htmlData{anchor=sum}{\\color{@sky}{4+6+9+10+11}}$"},{"latex":"$$\\htmlData{anchor=total}{\\color{@sky}{40}}$"}],"highlights":[{"color":"sky","style":"text-color-with-background","anchor":"sum"}],"connections":[{"to":"total","from":"sum","color":"sky","label":"add"}]},"order":1,"title":"Add the numbers","description":"Add every number in the list. Correctly finding this total earns the method mark, M1."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\text{Mean}=\\htmlData{anchor=division}{\\color{@amber}{40\\div5}}$"},{"latex":"$$\\text{Mean}=\\htmlData{anchor=answer}{\\color{@green}{8}}$"}],"highlights":[{"color":"green","style":"text-color-with-background","anchor":"answer"}],"connections":[{"to":"answer","from":"division","color":"green","label":"divide"}]},"order":2,"title":"Divide by five","description":"Divide the total by the number of values. The correct mean earns A1."}]}],"generatedAt":"2026-07-20T16:27:34.824Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":64},"walkthroughVideo":null},{"id":"185b8ab9-2b50-4391-ac86-231fc4ed177a","revisionId":"3d70fed1-1a81-4564-a208-2c94a3b4557c","questionNumber":"3","questionType":"LA","specification":"Here are the heights, in cm, of 8 people.\n\n155 171 164 171 167 188 190 151","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}],"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"]}]