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{"name": "Calculate centred moving averages", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "variables": {"tol": {"templateType": "anything", "group": "Ungrouped variables", "definition": "0", "description": "", "name": "tol"}, "tothere3": {"templateType": "anything", "group": "Ungrouped variables", "definition": "if(ch=3,random(\"Mesa Airways.\",\"KiwiJet.\",\"Frontier Airlines.\",\"EasyAir.\",\"RyanJet.\",\"HorizonAir.\",\"SunCity Airlines.\",\"Air Caribe.\"),\"\")", "description": "", "name": "tothere3"}, "tothere": {"templateType": "anything", "group": "Ungrouped variables", "definition": "if(ch=1,random(\"Souter Lighthouse\", \"Washington Old Hall\",\"Gibside\",\"Cherryburn Cottage\",\"Lindisfarne Castle\",\"Oakhurst Cottage\",\"George Stephenson's Birthplace\",\"Holy 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"anything", "group": "Ungrouped variables", "definition": "random(750..1050#50)", "description": "", "name": "j7"}, "m8": {"templateType": "anything", "group": "Ungrouped variables", "definition": "m7+random(20..70#10)", "description": "", "name": "m8"}, "y4": {"templateType": "anything", "group": "Ungrouped variables", "definition": "(ap7+2*(m7+j7+ja8)+ap8)/8", "description": "", "name": "y4"}}, "ungrouped_variables": ["ch", "j8", "j9", "tothere3", "j7", "tothere4", "y9", "y8", "ap9", "y3", "y5", "y4", "y7", "y6", "rows", "m7", "tol", "m9", "m8", "ap8", "tothere2", "nat", "ap7", "ja8", "ja9", "this", "ja7", "tol1", "tothere", "y10"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "name": "Calculate centred moving averages", "functions": {}, "showQuestionGroupNames": false, "parts": [{"scripts": {}, "gaps": [{"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "y3+tol", "minValue": "y3-tol", "correctAnswerFraction": false, "marks": 1, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "y4+tol", "minValue": "y4-tol", "correctAnswerFraction": false, "marks": 1, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "y5+tol", "minValue": "y5-tol", "correctAnswerFraction": false, "marks": 1, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "y6+tol", "minValue": "y6-tol", "correctAnswerFraction": false, "marks": 1, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "y7+tol", "minValue": "y7-tol", "correctAnswerFraction": false, "marks": 1, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "y8+tol", "minValue": "y8-tol", "correctAnswerFraction": false, "marks": 1, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "y9+tol", "minValue": "y9-tol", "correctAnswerFraction": false, "marks": 1, "showPrecisionHint": false}, {"showCorrectAnswer": true, "allowFractions": false, "scripts": {}, "type": "numberentry", "maxValue": "y10+tol", "minValue": "y10-tol", "correctAnswerFraction": false, "marks": 1, "showPrecisionHint": false}], "type": "gapfill", "prompt": "<p>Find the series of (centred) moving averages for these data and complete the table below:</p>\n<table border=\"1\">\n<tbody>\n<tr><th align=\"left\"></th><th>Jan-Mar</th><th>April-June</th><th>July-Sep</th><th>Oct-Dec</th></tr>\n<tr><th align=\"left\">2007</th>\n<td>*</td>\n<td>*</td>\n<td>[[0]]</td>\n<td>[[1]]</td>\n</tr>\n<tr><th align=\"left\">2008</th>\n<td>[[2]]</td>\n<td>[[3]]</td>\n<td>[[4]]</td>\n<td>[[5]]</td>\n</tr>\n<tr><th align=\"left\">2009</th>\n<td>[[6]]</td>\n<td>[[7]]</td>\n<td>*</td>\n<td>*</td>\n</tr>\n</tbody>\n</table>", "showCorrectAnswer": true, "marks": 0}], "statement": "<p>The following tables shows by quarter over the three years 2007, 2008, 2009 {This} {tothere} {nat} {tothere2} {tothere3} {tothere4}&nbsp;</p>\n<p>{table(rows,[\" \",\"Jan-Mar\",\"Apr-June\",\"July-Sep\",\"Oct-Dec\"])}</p>", "tags": ["ACE2013", "centred moving averages", "checked2015", "moving average", "statistics", "time series"], "rulesets": {}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "<p><strong>22/03/2014:</strong></p>\n<p><strong><br /></strong>Created from ACE i-assess question.</p>", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>Centred moving averages.</p>"}, "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "<table border=\"1\">\n<tbody>\n<tr><th align=\"left\"></th><th>Jan-Mar</th><th>April-June</th><th>July-Sep</th><th>Oct-Dec</th></tr>\n<tr><th align=\"left\">2007</th>\n<td>*</td>\n<td>*</td>\n<td>$\\var{y3}$</td>\n<td>$\\var{y4}$</td>\n</tr>\n<tr><th align=\"left\">2008</th>\n<td>$\\var{y5}$</td>\n<td>$\\var{y6}$</td>\n<td>$\\var{y7}$</td>\n<td>$\\var{y8}$</td>\n</tr>\n<tr><th align=\"left\">2009</th>\n<td>$\\var{y9}$</td>\n<td>$\\var{y10}$</td>\n<td>*</td>\n<td>*</td>\n</tr>\n</tbody>\n</table>\n<p>Let $Y_t$ denote the data table values so $Y_1=\\var{ja7},\\;Y_2=\\var{ap7} ,\\ldots, Y_{12}=\\var{j9}$</p>\n<p>Using the centred moving average formula for quarters:</p>\n<p>\\[Y^*_t=\\frac{Y_{t-2}+2(Y_{t-1}+Y_t+Y_{t+1})+Y_{t+2}}{8}\\] we obtain the values in the table above.</p>\n<p>Thus the moving average for Oct-Dec 2007 is:</p>\n<p>\\[\\frac{Y_{2}+2(Y_{3}+Y_4+Y_{5})+Y_{6}}{8}=\\frac{\\var{ap7} + 2 (\\var{m7} + \\var{j7} + \\var{ja8}) + \\var{ap8}}{8} = \\var{y4}\\]</p>\n<p></p>", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}