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{"name": "Identifying Parts of Equations: r", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": [], "name": "Identifying Parts of Equations: r", "tags": [], "advice": "", "rulesets": {}, "parts": [{"prompt": "<p>What is $\\bar{x}$?</p>", "matrix": ["1", 0, 0, 0], "shuffleChoices": true, "marks": 0, "variableReplacements": [], "choices": ["<p>Sample mean</p>", "<p>Sample variance</p>", "<p>Sum of the observation values</p>", "<p>Population variance</p>"], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "maxMarks": "1", "scripts": {}, "distractors": ["", "", "", ""], "displayColumns": 0, "showCorrectAnswer": true, "type": "1_n_2", "minMarks": 0}, {"prompt": "<p>The term $\\sum(x_i - \\bar{x})^2$ can be written in a different form. Select the alternative form in the list below.</p>", "matrix": ["1", 0, 0, 0], "shuffleChoices": true, "marks": 0, "variableReplacements": [], "choices": ["<p>$\\sum({x_i}^2- 2x_i\\bar{x} + \\bar{x}^2)$</p>", "<p>$\\sum(x_i-\\bar{x})\\times\\sum(x_i-\\bar{x})$</p>", "<p>$\\sum({x_i}^2 + \\bar{x}^2)$</p>", "<p>$\\sum({x_i}^2 - \\bar{x}^2)$</p>"], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "maxMarks": 0, "scripts": {}, "distractors": ["", "", "", ""], "displayColumns": 0, "showCorrectAnswer": true, "type": "1_n_2", "minMarks": 0}, {"prompt": "<p>What does $x_i-\\bar{x}$ mean?</p>", "matrix": ["1", 0, 0], "shuffleChoices": true, "marks": 0, "variableReplacements": [], "choices": ["<p>The amount observation $i$ deviated from the sample mean.</p>", "<p>The difference between the population&nbsp;mean and the observation.</p>", "<p>The amount observation are larger than the sample mean by.</p>"], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "maxMarks": 0, "scripts": {}, "distractors": ["", "", ""], "displayColumns": "1", "showCorrectAnswer": true, "type": "1_n_2", "minMarks": 0}], "statement": "<p>Given the formula</p>\n<p>$r = \\frac{\\sum(x_i-\\bar{x})(y_i-\\bar{y})}{\\sqrt{\\sum(x_i-\\bar{x})^2\\sum(y_i - \\bar{y})^2}}$</p>\n<p>answer the following questions.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {}, "metadata": {"notes": "", "description": "<p>Identify the parts of a statistical&nbsp;formula</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Hayley Moore", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/495/"}]}]}], "contributors": [{"name": "Hayley Moore", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/495/"}]}