// Numbas version: exam_results_page_options
{"name": "Numerical reasoning - data table", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {"pretendinput": {"definition": "return $('<input type=\"text\" disabled/>').attr('value',val);", "type": "html", "parameters": [["val", "number"]], "language": "javascript"}}, "ungrouped_variables": ["alphas", "biggest3to4", "biggestpercent4to5", "deltas", "deltatranspose", "diffs1to5", "incomes", "names", "originalnames", "percents1to4", "percents4to5", "smallest1to5", "smallestpercent1to4", "q"], "name": "Numerical reasoning - data table", "tags": ["data table", "maths-aid", "numerical reasoning", "percentage"], "type": "question", "advice": "", "rulesets": {}, "parts": [{"stepsPenalty": 0, "displayColumns": 0, "prompt": "<p>Which industry had the largest increase in the euro amount of income from&nbsp;<strong>Year 3</strong>&nbsp;to&nbsp;<strong>Year 4</strong>?</p>", "matrix": ["if(deltas[2][0]=biggest3to4,1,0)", "if(deltas[2][1]=biggest3to4,1,0)", "if(deltas[2][2]=biggest3to4,1,0)", "if(deltas[2][3]=biggest3to4,1,0)", "if(deltas[2][4]=biggest3to4,1,0)", "if(deltas[2][5]=biggest3to4,1,0)"], "shuffleChoices": false, "scripts": {}, "choices": ["{names[0]}", "{names[1]}", "{names[2]}", "{names[3]}", "{names[4]}", "{names[5]}"], "marks": 0, "displayType": "radiogroup", "maxMarks": 0, "distractors": ["", "", "", "", "", ""], "steps": [{"type": "information", "showCorrectAnswer": true, "marks": 0, "prompt": "<p>For example, {names[0]} had an increase of $\\simplify[]{{incomes[0][3]} - {incomes[0][2]} = {deltas[2][0]}}$ billion euros from year 3 to year 4.</p>\n            <p>Write the increase for each industry (in billions of euros) and find the largest:</p>\n            <table>\n            <tbody>\n            <tr>\n            <td><strong>{names[0]}</strong></td>\n            <td>increase = {pretendinput(deltas[2][0])} billion euros</td>\n            </tr>\n            <tr>\n            <td><strong>{names[1]}</strong></td>\n            <td>increase = [[0]] billion euros</td>\n            </tr>\n            <tr>\n            <td><strong>{names[2]}</strong></td>\n            <td>increase = [[1]] billion euros</td>\n            </tr>\n            <tr>\n            <td><strong>{names[3]}</strong></td>\n            <td>increase = [[2]] billion euros</td>\n            </tr>\n            <tr>\n            <td><strong>{names[4]}</strong></td>\n            <td>increase = [[3]] billion euros</td>\n            </tr>\n            <tr>\n            <td><strong>{names[5]}</strong></td>\n            <td>increase = [[4]] billion euros</td>\n            </tr>\n            </tbody>\n            </table>", "scripts": {}}], "showCorrectAnswer": true, "type": "1_n_2", "minMarks": 0}, {"stepsPenalty": 0, "displayColumns": 0, "prompt": "<p>{table(map([names[j]]+incomes[j],j,0..5),['Industry','Year 1','Year 2','Year 3','Year 4','Year 5'])}</p>\n      <p>Which country had the smallest increase in the euro amount of income from <strong>Year 1</strong> to <strong>Year 5</strong>?</p>", "matrix": ["if(diffs1to5[0]=smallest1to5,1,0)", "if(diffs1to5[1]=smallest1to5,1,0)", "if(diffs1to5[2]=smallest1to5,1,0)", "if(diffs1to5[3]=smallest1to5,1,0)", "if(diffs1to5[4]=smallest1to5,1,0)", "if(diffs1to5[5]=smallest1to5,1,0)"], "shuffleChoices": false, "scripts": {}, "choices": ["{names[0]}", "{names[1]}", "{names[2]}", "{names[3]}", "{names[4]}", "{names[5]}"], "marks": 0, "displayType": "radiogroup", "maxMarks": 0, "distractors": ["", "", "", "", "", ""], "steps": [{"type": "information", "showCorrectAnswer": true, "marks": 0, "prompt": "<p>For example, {names[0]} had an increase of $\\simplify[]{{incomes[0][4]}-{incomes[0][0]} = {diffs1to5[0]}}$ billion euros from year 1 to year 5.</p>\n          <p>Write the increase for each industry (in billions of euros) and find the smallest:</p>\n          <table>\n          <tbody>\n          <tr>\n          <td><strong>{names[0]}</strong></td>\n          <td>increase = {pretendinput(diffs1to5[0])} billion euros</td>\n          </tr>\n          <tr>\n          <td><strong>{names[1]}</strong></td>\n          <td>increase = [[0]] billion euros</td>\n          </tr>\n          <tr>\n          <td><strong>{names[2]}</strong></td>\n          <td>increase = [[1]] billion euros</td>\n          </tr>\n          <tr>\n          <td><strong>{names[3]}</strong></td>\n          <td>increase = [[2]] billion euros</td>\n          </tr>\n          <tr>\n          <td><strong>{names[4]}</strong></td>\n          <td>increase = [[3]] billion euros</td>\n          </tr>\n          <tr>\n          <td><strong>{names[5]}</strong></td>\n          <td>increase = [[4]] billion euros</td>\n          </tr>\n          </tbody>\n          </table>", "scripts": {}}], "showCorrectAnswer": true, "type": "1_n_2", "minMarks": 0}, {"stepsPenalty": 0, "displayColumns": 0, "prompt": "<p>{table(map([names[j]]+incomes[j],j,0..5),['Industry','Year 1','Year 2','Year 3','Year 4','Year 5'])}</p>\n      <p>Which industry experienced the largest percentage increase from Year 4 to Year 5?</p>", "matrix": ["if(percents4to5[0]=biggestpercent4to5,1,0)", "if(percents4to5[1]=biggestpercent4to5,1,0)", "if(percents4to5[2]=biggestpercent4to5,1,0)", "if(percents4to5[3]=biggestpercent4to5,1,0)", "if(percents4to5[4]=biggestpercent4to5,1,0)", "if(percents4to5[5]=biggestpercent4to5,1,0)"], "shuffleChoices": false, "scripts": {}, "choices": ["{names[0]}", "{names[1]}", "{names[2]}", "{names[3]}", "{names[4]}", "{names[5]}"], "marks": 0, "displayType": "radiogroup", "maxMarks": 0, "distractors": ["", "", "", "", "", ""], "steps": [{"type": "information", "showCorrectAnswer": true, "marks": 0, "prompt": "<p>This means that you have to work out the increase from year 4 to year 5 as a percentage of the income in year 4 for each industry and find the biggest percentage increase.</p>\n            <p>For example, {names[1]} had an increase of {deltas[3][1]} billion euros from {incomes[1][3]} in year 4 to year 5. The percentage increase was therefore</p>\n            <p>\\[ \\frac{\\var{deltas[3][1]}}{\\var{incomes[1][3]}} \\times 100\\% = \\var{precround(percents4to5[1],2)}\\% \\]</p>\n            <p>to two decimal places.</p>\n            <p>(Calculating to one decimal place would probably have been enough - but it's possible that there are two industries with the same percentage increase to one decimal place.)</p>\n            <p>Find the percentage increase (in billions of euros) and find the largest</p>\n            <table>\n            <tbody>\n            <tr>\n            <td><strong>{names[0]}</strong></td>\n            <td>% increase = [[0]]%</td>\n            </tr>\n            <tr>\n            <td><strong>{names[1]}</strong></td>\n            <td>% increase = {pretendinput(precround(percents4to5[1],2))}%</td>\n            </tr>\n            <tr>\n            <td><strong>{names[2]}</strong></td>\n            <td>% increase = [[1]]%</td>\n            </tr>\n            <tr>\n            <td><strong>{names[3]}</strong></td>\n            <td>% increase = [[2]]%</td>\n            </tr>\n            <tr>\n            <td><strong>{names[4]}</strong></td>\n            <td>% increase = [[3]]%</td>\n            </tr>\n            <tr>\n            <td><strong>{names[5]}</strong></td>\n            <td>% increase = [[4]]%</td>\n            </tr>\n            </tbody>\n            </table>", "scripts": {}}], "showCorrectAnswer": true, "type": "1_n_2", "minMarks": 0}, {"stepsPenalty": 0, "displayColumns": 0, "prompt": "<p>{table(map([names[j]]+incomes[j],j,0..5),['Industry','Year 1','Year 2','Year 3','Year 4','Year 5'])}</p>\n      <p>Which industry had the least percentage change from Year 1 to Year 4?</p>", "matrix": ["if(percents1to4[0]=smallestpercent1to4,1,0)", "if(percents1to4[1]=smallestpercent1to4,1,0)", "if(percents1to4[2]=smallestpercent1to4,1,0)", "if(percents1to4[3]=smallestpercent1to4,1,0)", "if(percents1to4[4]=smallestpercent1to4,1,0)", "if(percents1to4[5]=smallestpercent1to4,1,0)"], "shuffleChoices": false, "scripts": {}, "choices": ["{names[0]}", "{names[1]}", "{names[2]}", "{names[3]}", "{names[4]}", "{names[5]}"], "marks": 0, "displayType": "radiogroup", "maxMarks": 0, "distractors": ["", "", "", "", "", ""], "steps": [{"type": "information", "showCorrectAnswer": true, "marks": 0, "prompt": "<p>This means that you have to work out the increase from year 1 to year 4 as a percentage of the income in year 1 for each industry and find the smallest percentage increase.</p>\n            <p>For example, {names[4]} had an increase of $\\simplify[]{{incomes[4][3]}-{incomes[4][0]} = {incomes[4][3]-incomes[4][0]}}$ billion euros from {incomes[4][0]} billion euros in year 1 to {incomes[4][3]} billion euros in year 4. The percentage increase was therefore</p>\n            <p>\\[ \\frac{\\var{incomes[4][3]-incomes[4][0]}}{\\var{incomes[4][0]}} \\times 100\\% = \\var{precround(percents1to4[4],2)}\\% \\]</p>\n            <p>to two decimal places.</p>\n            <p>(Once again taking the percentage to two decimal places to be on the safe side.)</p>\n            <p>Find the percentage change for each industry and find the least</p>\n            <table>\n            <tbody>\n            <tr>\n            <td><strong>{names[0]}</strong></td>\n            <td>% increase = [[0]]%</td>\n            </tr>\n            <tr>\n            <td><strong>{names[1]}</strong></td>\n            <td>% increase = [[1]]%</td>\n            </tr>\n            <tr>\n            <td><strong>{names[2]}</strong></td>\n            <td>% increase = [[2]]%</td>\n            </tr>\n            <tr>\n            <td><strong>{names[3]}</strong></td>\n            <td>% increase = [[3]]%</td>\n            </tr>\n            <tr>\n            <td><strong>{names[4]}</strong></td>\n            <td>% increase = {pretendinput(precround(percents1to4[4],2))}%</td>\n            </tr>\n            <tr>\n            <td><strong>{names[5]}</strong></td>\n            <td>% increase = [[4]]%</td>\n            </tr>\n            </tbody>\n            </table>", "scripts": {}}], "showCorrectAnswer": true, "type": "1_n_2", "minMarks": 0}], "statement": "<p>The following table describes the income of various industries over a five year period.&nbsp;</p>\n  <h3 style=\"text-align: center;\">Income of industries (in billions of euros)</h3>\n  <p>{table(map([names[j]]+incomes[j],j,0..5),['Industry','Year 1','Year 2','Year 3','Year 4','Year 5'])}</p>\n  <p>There are four parts to this question; click on the&nbsp;<strong>Show steps</strong> button if you need help with any part.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"biggest3to4": {"definition": "max(deltas[2])", "templateType": "anything", "group": "Ungrouped variables", "name": "biggest3to4", "description": ""}, "alphas": {"definition": "repeat(random(10..200),6)", "templateType": "anything", "group": "Ungrouped variables", "name": "alphas", "description": ""}, "originalnames": {"definition": "['Financial Services','Telecommunications','Engineering','Agriculture','Manufacturing','Transportation','Computing','Utilities','Retail']", "templateType": "anything", "group": "Ungrouped variables", "name": "originalnames", "description": ""}, "deltas": {"definition": "//differences in income for each year. \n    //[i,j] is industry j's delta for year i\n    repeat(deal(20)[0..6],4)", "templateType": "anything", "group": "Ungrouped variables", "name": "deltas", "description": ""}, "incomes": {"definition": "map(map(alphas[j]+sum(deltatranspose[j][0..k]),k,0..4),j,0..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "incomes", "description": ""}, "smallestpercent1to4": {"definition": "min(percents1to4)", "templateType": "anything", "group": "Ungrouped variables", "name": "smallestpercent1to4", "description": ""}, "diffs1to5": {"definition": "map(sum(deltatranspose[j]),j,0..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "diffs1to5", "description": ""}, "q": {"definition": "join(percents1to4,',')", "templateType": "anything", "group": "Ungrouped variables", "name": "q", "description": ""}, "percents4to5": {"definition": "map(100*(income[4]/income[3]-1),income,incomes)", "templateType": "anything", "group": "Ungrouped variables", "name": "percents4to5", "description": ""}, "names": {"definition": "shuffle(originalnames)[0..6]", "templateType": "anything", "group": "Ungrouped variables", "name": "names", "description": ""}, "deltatranspose": {"definition": "//rows are each industry's deltas, so they can be summed more easily\n    list(transpose(matrix(deltas)))", "templateType": "anything", "group": "Ungrouped variables", "name": "deltatranspose", "description": ""}, "percents1to4": {"definition": "map(100*(income[3]/income[0]-1),income,incomes)", "templateType": "anything", "group": "Ungrouped variables", "name": "percents1to4", "description": ""}, "biggestpercent4to5": {"definition": "max(percents4to5)", "templateType": "anything", "group": "Ungrouped variables", "name": "biggestpercent4to5", "description": ""}, "smallest1to5": {"definition": "min(diffs1to5)", "templateType": "anything", "group": "Ungrouped variables", "name": "smallest1to5", "description": ""}}, "metadata": {"notes": "<p>Incomes are generated as follows:</p>\n    <ul>\n    <li>for each industry, an initial income is generated and stored in the array \"alphas\".</li>\n    </ul>", "description": "<p>Following part 2, \"Questions on Data Tables\", from the Maths Aid workbook \"Numerical reasoning tests\".</p>\n                                <p>Only doing the first 4 questions because the others involve trends that need lots more thinking about how to randomise.</p>\n                                <p>Not finished!</p>", "licence": "Creative Commons Attribution 4.0 International"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}]}