":"Question Set 2: Measures of Location and Spread","calculatorUse":null,"isCalculation":true,"parts":[{"id":"4df74f5a-0b27-4428-8a1d-ab3fc9b410c2","label":"0","content":"Calculate the mean and the standard deviation for these data.","markscheme":"- Mean: $\\bar{x} = \\frac{1587}{70} = 22.7$ B1\n- Standard Deviation: $\\sigma = \\sqrt{\\frac{4879}{70}}$ M1\n- Final answer $8.35$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Correct calculation of the mean ($22.7$).","code":"B"},{"id":"p2","marks":1,"description":"Correct method for standard deviation using $S_{xx}$.","code":"M"},{"id":"p3","marks":1,"description":"Final answer for standard deviation of $8.35$.","code":"A"}],"finalAnswers":["22.7","8.35"],"generatedAt":"2026-05-12T02:14:06.549Z","modelVersion":"gemini-3-flash-preview"},"tableImages":[],"explanation":{"methods":[{"id":"summary_statistics","label":"Use summary statistics","steps":[{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\bar{x}=\\dfrac{\\htmlData{anchor=sumx}{\\color{@sky}{\\sum x}}}{\\htmlData{anchor=nmean}{\\color{@amber}{n}}}$"},{"latex":"$$\\bar{x}=\\dfrac{\\htmlData{anchor=sumvalue}{\\color{@sky}{1587}}}{\\htmlData{anchor=nvalue}{\\color{@amber}{70}}}$"},{"latex":"$$\\bar{x}=\\htmlData{anchor=meanraw}{\\color{@green}{22.671428\\ldots}}$"},{"latex":"$$\\bar{x}=\\htmlData{anchor=meanrounded}{\\color{@green}{22.7}}$"}],"highlights":[{"color":"green","style":"text-color-with-background","anchor":"meanrounded"}],"connections":[{"to":"sumvalue","from":"sumx","color":"sky","label":"substitute"},{"to":"nvalue","from":"nmean","color":"amber","label":"substitute"},{"to":"meanrounded","from":"meanraw","color":"green","label":"round"}]},"order":1,"title":"Calculate the mean","description":"Substitute the given total and number of teachers. The correctly rounded mean earns the B1 mark."},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\htmlData{anchor=sd_formula}{\\color{@sky}{\\sigma=\\sqrt{\\frac{S_{xx}}{n}}}}$"},{"latex":"$$\\htmlData{anchor=sd_substitution}{\\color{@sky}{\\sigma=\\sqrt{\\frac{4879}{70}}}}$"},{"latex":"$$\\htmlData{anchor=sd_answer}{\\color{@green}{\\sigma\\approx 8.35}}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"sd_substitution"},{"color":"green","style":"text-color-with-background","anchor":"sd_answer"}],"connections":[{"to":"sd_substitution","from":"sd_formula","color":"sky","label":"substitute"},{"to":"sd_answer","from":"sd_substitution","color":"green","label":"calculate and round"}]},"order":2,"title":"Calculate the spread","description":"Frank asked every teacher, so the data cover the whole population and we divide Sₓₓ by n. The substitution earns M1 and 8.35 earns A1."}]}],"generatedAt":"2026-07-20T16:24:35.644Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]}],"options":[],"explanation":null,"firstAttemptFullMarks":{"percent":68},"walkthroughVideo":null},{"id":"4637db17-269c-4880-82dc-834f00ca414b","revisionId":"54aeb775-5ee8-44aa-9a48-d43364a8f4fb","questionNumber":"7","questionType":"LA","specification":"30 people ran a race and their race times, $x$, were recorded.\n\nFor these people $\\sum x = 466 \\quad \\sum x^2 = 7592$","difficulty":1,"difficultyBand":"easy","totalMarks":3,"sourceTitle":"Question Set 2: Measures of Location and Spread","calculatorUse":null,"isCalculation":true,"parts":[{"id":"7fe95c2f-61d1-4510-b9d9-ed5992698db6","label":"0","content":"Calculate the mean and the standard deviation for these data.","markscheme":"- Mean: $\\bar{x} = \\frac{466}{30} = 15.5$ B1\n- Standard Deviation: $\\sigma = \\sqrt{\\frac{7592}{30} - 15.5^2}$ M1\n- Final answer $3.43$ A1","marks":3,"order":0,"markingRubric":{"totalMarks":3,"points":[{"id":"p1","marks":1,"description":"Correct calculation of the mean ($15.5$).","code":"B"},{"id":"p2","marks":1,"description":"Correct method for standard deviation.","code":"M"},{"id":"p3","marks":1,"description":"Final answer for standard de

Measures of Location and Spread

Question 2

Measures of Location and Spread Questions

Measures of Location and Spread

Question 2

Measures of Location and Spread Questions