riginal Mean} + \\text{Average Deviation} \\\\ &= 74 + 1.5714... \\\\ &\\approx 75.5714... \\end{aligned}$$","calculator":[{"gdc":{"expression":"74 + 11 / 7","instructions":"Input the calculation directly on the main run menu."},"ti84":{"expression":"74 + 11 / 7","instructions":"Type the expression into the home screen and press ENTER."},"desmos":{"expression":"74 + 11 / 7","instructions":"Type the formula to see the decimal value instantly."},"description":"Calculate the new mean by adding the average deviation directly to the original mean."}]},{"type":"text","order":3,"title":"Round and verify","content":"Rounding our answer to 1 decimal place gives:\n\n$$\\text{New Mean} \\approx 75.6$$\n\n### How this relates to the Markscheme:\nOn your exam, you can show either this deviation method or the total sum method to earn full marks:\n1. **Total score for 6 quizzes**: $74 \\times 6 = 444$ M1\n2. **Total score for 7 quizzes**: $444 + 85 = 529$ M1\n3. **Final Mean**: $529 \\div 7 \\approx 75.6$ (to 1 d.p.) A1\n\nBoth methods lead to the exact same result, but the deviation method lets you work with much smaller numbers and is easier to calculate mentally!"}]}],"generatedAt":"2026-06-12T18:52:32.304Z","modelVersion":"gemini-3.5-flash","explanationVersion":"v2"},"firstAttemptFullMarks":{"percent":52},"walkthroughVideo":{"url":"https://assets.mathsgenie.co.uk/walkthroughs/videos/67542adc-8786-4b33-be92-87b13c6ddf25.mp4","durationSeconds":115,"posterUrl":"https://assets.mathsgenie.co.uk/walkthroughs/videos/67542adc-8786-4b33-be92-87b13c6ddf25.jpg"}},{"id":"8dbb971c-04b2-4a9b-8c73-400007bdecb8","revisionId":"ec3522ca-5e63-4278-abe5-ca38455fc5f9","questionNumber":null,"questionType":"LA","specification":"Here are the scores of seven students in a spelling test.\n\n12 8 15 6 12 10 7","difficulty":2,"difficultyBand":"medium","totalMarks":5,"sourceTitle":null,"calculatorUse":"non_calc","isCalculation":true,"parts":[{"id":"619a361c-494d-42a4-ad78-df1736d7b2e0","label":"a","content":"Find the range.","markscheme":"- Identifying the highest and lowest values or showing the calculation: $15 - 6$ M1\n- $9$ A1","marks":2,"order":0,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Evidence of identifying 15 and 6 or writing $15 - 6$.","code":"M"},{"id":"p2","marks":1,"description":"Correct range of 9.","code":"A"}],"finalAnswers":["9"],"generatedAt":"2026-05-06T14:02:42.822Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"highest_minus_lowest","label":"Highest minus lowest","steps":[{"type":"text","order":0,"title":"Identify the extremes","content":"The highest score is $15$ and the lowest score is $6$. Identifying both extreme values earns **M1**.","highlights":[{"text":"15","location":"specification"},{"text":"6","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\operatorname{range}=\\htmlData{anchor=calculation}{\\color{@sky}{15}-\\color{@orange}{6}}$"},{"latex":"$$\\operatorname{range}=\\htmlData{anchor=result}{\\color{@green}{9}}$"}],"highlights":[{"color":"sky","style":"text-color-with-background","anchor":"calculation"},{"color":"green","style":"text-color-with-background","anchor":"result"}],"connections":[{"to":"result","from":"calculation","color":"green","label":"subtract"}]},"order":1,"title":"Subtract the lowest","description":"Subtract the lowest score from the highest score. The correct value, 9, earns A1."}]}],"generatedAt":"2026-07-19T16:42:40.563Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]},{"id":"745441b5-130d-4a5b-b0bb-d8662af958d5","label":"b","content":"Calculate the mean.","markscheme":"- Sum of numbers: $12 + 8 + 15 + 6 + 12 + 10 + 7 = 70$ M1\n- Mean: $70 \\div 7 = 10$ A1","marks":2,"order":1,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Sum of the seven numbers divided by 7.","code":"M"},{"id":"p2","marks":1,"description":"Correct mean of 10.","code":"

Averages

Question 8

Averages Questions

Averages

Question 8

Averages Questions