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method mark for finding the sum of (points $\\times$ frequency): $0 \\times 9 + 1 \\times 11 + 2 \\times 18 + 3 \\times 7 + 4 \\times 4 + 5 \\times 1 = 89$ M1\n- Award method mark for dividing the total points by the total frequency: $89 \\div 50$ M1\n- Final answer of 1.78 A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Calculates the total number of points (89) by summing products of points and frequency.","code":"M"},{"id":"p2","marks":1,"description":"Divides the total points by the total frequency (50).","code":"M"},{"id":"p3","marks":1,"description":"Final answer of 1.78.","code":"A"}],"finalAnswers":["1.78"],"generatedAt":"2026-05-07T01:48:24.436Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"frequency_table_mean","label":"Find the mean","steps":[{"type":"text","order":0,"title":"Recall the mean","content":"For a frequency table, first multiply each points value by its frequency. This gives the total points contributed by that row. Then use\n\n$$\\text{mean}=\\frac{\\text{total points}}{\\text{total number of games}}.$$","highlights":[{"text":"mean number of points per game","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$T=\\htmlData{anchor=products}{\\color{@sky}{(0\\times9)+(1\\times11)+(2\\times18)+(3\\times7)+(4\\times4)+(5\\times1)}}$"},{"latex":"$$T=\\htmlData{anchor=values}{\\color{@orange}{0+11+36+21+16+5}}$"},{"latex":"$$T=\\htmlData{anchor=total}{\\color{@green}{89}}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"products"},{"color":"orange","style":"text-color","anchor":"values"},{"color":"green","style":"text-color-with-background","anchor":"total"}]},"order":1,"title":"Find total points","description":"Multiply each points value by its frequency, then add the results. Writing this complete calculation earns the first method mark (M1)."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$N=\\htmlData{anchor=frequencies}{\\color{@orange}{9+11+18+7+4+1}}$"},{"latex":"$$N=\\htmlData{anchor=games}{\\color{@green}{50}}$"}],"highlights":[{"color":"orange","style":"text-color","anchor":"frequencies"},{"color":"green","style":"text-color-with-background","anchor":"games"}]},"order":2,"title":"Count the games","description":"Add the frequencies because each frequency tells you how many games had that score."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\operatorname{mean}=\\htmlData{anchor=division}{\\color{@sky}{\\dfrac{89}{50}}}$"},{"latex":"$$\\operatorname{mean}=\\htmlData{anchor=answer}{\\color{@green}{1.78\\text{ points per game}}}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"division"},{"color":"green","style":"text-color-with-background","anchor":"answer"}]},"order":3,"title":"Calculate the mean","description":"Divide the total points by the total number of games. Setting up this division earns the second method mark (M1), and the correct result earns the accuracy mark (A1)."}]}],"generatedAt":"2026-07-20T16:25:44.936Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":52},"walkthroughVideo":null},{"id":"8bd84479-708f-43a9-8927-19c298613ac7","revisionId":"c9684fc1-3083-4d1c-a314-4393925bd759","questionNumber":"2","questionType":"LA","specification":"The table shows information about the number of goals scored per game by a football team.\n\n| Goals | Frequency |\n| :--- | :--- |\n| 0 | 10 |\n| 1 | 12 |\n| 2 | $x$ |\n| 3 | 7 |\n| 4 or more | 0 |","difficulty":2,"difficultyBand":"medium","totalMarks":3,"sourceTitle":"Averages from Frequency Tables","calculatorUse":null,"isCalculation":true,"parts":[{"id":"0a00bc90-7f5e-4f00-9b57-fd10c2ae2756","label":"0","content":"The team scored a total of 55 goals. Find the value of $x$.","markscheme":"- Award method mark for setting up an equation for the total goals: $(0 \\times 10) + (1 \\times 12) + (2 \\times x) + (3 \\times 7) = 55$ M1\n- Award method mark for simplifying the equation: $12 + 2x + 21 = 55 \\Rightarrow 2x + 33 = 55$ M1\n- Final answer $x = 11$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Forms an expression or equation for the total goals involving $x$.","code":"M"},{"id":"p2","marks":1,"description":"Simplifies the equation to $2x = 22$ or equivalent.","code":"M"},{"id":"p3","marks":1,"description":"Finds $x = 11$.","code":"A"}],"finalAnswers":["11"],"generatedAt":"2026-05-07T01:48:24.436Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":null,"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":41},"walkthroughVideo":null}],"subjectCode":"igcse_maths__oxford_aqa","summaries":[{"id":"a59093a9-63bd-4694-b3d1-3fedbbc81b39","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"8bd84479-708f-43a9-8927-19c298613ac7","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"9653f88e-0862-4773-8847-da413311f920","difficultyBand":"medium","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"a358a697-7d0e-4762-a5ab-8dbafd47c46f","difficultyBand":"medium","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"ba64f808-a9df-4102-846f-72fd43b3c7f8","difficultyBand":"medium","calculatorUse":null,"totalMarks":4,"questionType":"LA","isCalculation":true},{"id":"2fa756e8-3dcd-499c-bdb5-c4f34ec81bea","difficultyBand":"medium","calculatorUse":null,"totalMarks":3,"questionType":"LA","isCalculation":true},{"id":"bff2097f-a6c5-4b29-bc70-0d32d880203b","difficultyBand":"medium","calculatorUse":null,"totalMarks":5,"questionType":"LA","isCalculation":true}],"title":"Averages from Frequency Tables","topicId":"efbcba48-09bc-4740-af2c-c5eceb30a629","topicSidebar":"$L3a","topicSlug":"grade-4-4-17-averages-from-frequency-tables","topicTitle":"Averages from Frequency Tables"}]}],"$L3b","$L3c"]}]