// Numbas version: finer_feedback_settings
{"duration": 0, "navigation": {"browse": true, "reverse": true, "showresultspage": "oncompletion", "preventleave": true, "allowregen": true, "showfrontpage": true, "onleave": {"action": "none", "message": ""}}, "timing": {"allowPause": true, "timeout": {"action": "none", "message": ""}, "timedwarning": {"action": "none", "message": ""}}, "feedback": {"allowrevealanswer": true, "showtotalmark": true, "showactualmark": true, "showanswerstate": true, "advicethreshold": 0, "feedbackmessages": [], "intro": "", "enterreviewmodeimmediately": true, "showexpectedanswerswhen": "inreview", "showpartfeedbackmessageswhen": "always", "showactualmarkwhen": "always", "showtotalmarkwhen": "always", "showanswerstatewhen": "always", "showadvicewhen": "never"}, "showstudentname": true, "percentPass": 0, "question_groups": [{"pickQuestions": 1, "pickingStrategy": "all-ordered", "name": "Group", "questions": [{"name": "Using a speed and acceleration graph", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Bradley Bush", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1521/"}], "variable_groups": [{"variables": ["a1", "b1", "c1", "d1", "z1", "f1"], "name": "speeds"}, {"variables": ["mab", "mbc", "mcd", "mde", "mef"], "name": "acceleration"}], "preamble": {"js": "", "css": ""}, "type": "question", "parts": [{"variableReplacementStrategy": "originalfirst", "type": "gapfill", "scripts": {}, "marks": 0, "showCorrectAnswer": true, "gaps": [{"maxMarks": 0, "type": "1_n_2", "showCorrectAnswer": true, "minMarks": 0, "distractors": ["", ""], "variableReplacementStrategy": "originalfirst", "displayType": "dropdownlist", "shuffleChoices": false, "showFeedbackIcon": true, "displayColumns": 0, "matrix": [0, "1"], "choices": ["<p>speed</p>", "<p>acceleration</p>"], "scripts": {}, "variableReplacements": [], "marks": 0}, {"maxMarks": 0, "type": "1_n_2", "showCorrectAnswer": true, "minMarks": 0, "distractors": ["", ""], "variableReplacementStrategy": "originalfirst", "displayType": "dropdownlist", "shuffleChoices": false, "showFeedbackIcon": true, "displayColumns": 0, "matrix": ["1", "0"], "choices": ["<p>speed</p>", "<p>acceleration</p>"], "scripts": {}, "variableReplacements": [], "marks": 0}], "variableReplacements": [], "showFeedbackIcon": true, "prompt": "<p>The green line with diamond shaped points maps the &nbsp;[[0]]&nbsp;of the car whilst the blue line with circular points maps the&nbsp;[[1]] of the car.</p>"}, {"variableReplacementStrategy": "originalfirst", "type": "gapfill", "scripts": {}, "marks": 0, "showCorrectAnswer": true, "gaps": [{"maxMarks": 0, "type": "1_n_2", "showCorrectAnswer": true, "minMarks": 0, "distractors": ["", ""], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "shuffleChoices": false, "showFeedbackIcon": true, "displayColumns": 0, "matrix": [0, "1"], "choices": ["<p>Yes - a car could have a negative speed.</p>", "<p>No - a car can never have a negative speed.</p>"], "scripts": {}, "variableReplacements": [], "marks": 0}], "variableReplacements": [], "showFeedbackIcon": true, "prompt": "<p>The graph shows no negative speeds; is there ever a case where the car could've had a negative speed? &nbsp;[[0]]</p>"}, {"variableReplacementStrategy": "originalfirst", "type": "gapfill", "scripts": {}, "marks": 0, "showCorrectAnswer": true, "gaps": [{"maxMarks": 0, "type": "1_n_2", "showCorrectAnswer": true, "minMarks": 0, "distractors": ["", ""], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "shuffleChoices": false, "showFeedbackIcon": true, "displayColumns": 0, "matrix": ["1", "0"], "choices": ["<p>Yes - a car could have a negative acceleration.</p>", "<p>No - a car can never have a negative acceleration.</p>"], "scripts": {}, "variableReplacements": [], "marks": 0}], "variableReplacements": [], "showFeedbackIcon": true, "prompt": "<p>The graph shows some negative accelerations; is it possible for a car to have negative acceleration? &nbsp;[[0]]</p>"}, {"variableReplacementStrategy": "originalfirst", "type": "gapfill", "scripts": {}, "marks": 0, "showCorrectAnswer": true, "gaps": [{"checkingtype": "absdiff", "type": "jme", "showCorrectAnswer": true, "vsetrange": [0, 1], "showpreview": true, "answer": "{mab}", "scripts": {}, "showFeedbackIcon": true, "checkvariablenames": false, "variableReplacementStrategy": "originalfirst", "vsetrangepoints": 5, "marks": 1, "checkingaccuracy": 0.001, "variableReplacements": [], "expectedvariablenames": []}], "variableReplacements": [], "showFeedbackIcon": true, "prompt": "<p>Calculate acceleration over the first $2$ seconds. Use the acceleration line on the graph to check your answer is correct.</p>\n<p>Acceleration $=$ &nbsp;[[0]] $m\\space/\\space s^2$</p>"}], "advice": "<h4>a)</h4>\n<p>We can analyse the nature of each line to find out which line resembles speed and which resembles acceleration.&nbsp;</p>\n<p></p>\n<p>The speed line should be distinguishable from the acceleration line based on the fact speed is always positive and has a continuous function (a line where the points are joined). This suggests the blue line with circular points represents speed.</p>\n<p>Where as acceleration can often be discontinuous and can be negative where speeds are decreasing. This suggests that the green line with diamond shaped points is the acceleration line.</p>\n<h4>b)</h4>\n<p>Speed is a scalar quantity without direction so speed is positive no matter the direction it travels in. Therefore our answer is \"no- a car can never have a negative speed.\".</p>\n<h4>c)</h4>\n<p>By defintion, when an object is slowing down it has a negative acceleration as the acceleration measures that change in speed. Therefore, our answer is \"yes- a car could have negative acceleration.\".</p>\n<h4>d)</h4>\n<p>To calculate acceleration we use the point at $0$ seconds, with a $0$ m/s speed and the point at $2$ seconds with a $\\var{b1}$ m/s speed and we find the gradient of the line between them. To find the gradient of a straight line we can use:</p>\n<p>\\[ <br/>\\begin{align}<br/>\\text{Gradient } &amp;= \\frac{y_1-y_2}{x_1-x_2}\\\\<br/>&amp;= \\frac{\\var{b1-a1}}{2-0}\\\\<br/>&amp;=\\simplify[fractionNumbers,simplifyFractions,unitDenominator]{{b1-a1}/2} \\text{.}<br/>\\end{align}<br/>\\]</p>\n<p>We can then compare the graph to our this answer in order to check that our calculation is correct and&nbsp;we see that we&nbsp;the same answer as was given.</p>\n<h4></h4>", "tags": ["acceleration", "graphs", "speed and acceleration graph", "taxonomy"], "variables": {"area": {"templateType": "anything", "description": "", "definition": "d2farea+c1*2+b1+c1+b1", "name": "area", "group": "Ungrouped variables"}, "d2farea": {"templateType": "anything", "description": "", "definition": "2*z1+d1+f1", "name": "d2farea", "group": "Ungrouped variables"}, "mab": {"templateType": "anything", "description": "", "definition": "(b1-a1)/2", "name": "mab", "group": "acceleration"}, "b1": {"templateType": "anything", "description": "", "definition": "random(6,8,10)+a1\n", "name": "b1", "group": "speeds"}, "mef": {"templateType": "anything", "description": "", "definition": "(f1-z1)/2", "name": "mef", "group": "acceleration"}, "a1": {"templateType": "anything", "description": "", "definition": "0\n", "name": "a1", "group": "speeds"}, "d1": {"templateType": "anything", "description": "", "definition": "c1", "name": "d1", "group": "speeds"}, "f1": {"templateType": "anything", "description": "", "definition": "2", "name": "f1", "group": "speeds"}, "c1": {"templateType": "anything", "description": "", "definition": "random(8,10,12,14)+b1", "name": "c1", "group": "speeds"}, "mde": {"templateType": "anything", "description": "", "definition": "(z1-d1)/2", "name": "mde", "group": "acceleration"}, "mbc": {"templateType": "anything", "description": "", "definition": "(c1-b1)/2", "name": "mbc", "group": "acceleration"}, "mcd": {"templateType": "anything", "description": "", "definition": "(d1-c1)/2", "name": "mcd", "group": "acceleration"}, "z1": {"templateType": "anything", "description": "", "definition": "c1-random(8,10,12)", "name": "z1", "group": "speeds"}}, "rulesets": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "functions": {}, "ungrouped_variables": ["d2farea", "area"], "statement": "<p>You are part of a team analysing a high speed car&nbsp;race. You are given the following graph mapping both the speed and acceleration of one particular car&nbsp;as it drives around a section of the race course. The horizontal axis plots time in seconds&nbsp;whilst the vertical axis maps speed and acceleration in metres per second and metres per second squared respectively.</p>\n<p style=\"text-align: center;\">{geogebra_applet('qEUWCdWt',[[\"a1\",a1],[\"b1\",b1],[\"c1\",c1],[\"d1\",d1],[\"z1\",z1],[\"f1\",f1]])}&nbsp;</p>", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>A graph shows both the speed and acceleration of a car. Identify which line corresponds to which measurement, and calculate the acceleration during a portion of time.</p>"}}, {"name": " Using a speed graph to find distance", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Bradley Bush", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1521/"}], "metadata": {"description": "<p>Use&nbsp;a piecewise linear graph of speed against time to find the distance travelled by a car.</p>\n<p>Finally, use the total distance travelled to find the average speed.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "rulesets": {}, "type": "question", "ungrouped_variables": ["d2farea", "area"], "advice": "<p>We can use a speed graph to calculate the distance travelled in a given time interval&nbsp;by finding the area under the line between the start and end times.</p>\n<h4>a)</h4>\n<p>The shape made by the speed curve, the line $x=0$, and the lines $t=4$&nbsp;and $t=6$ seconds is a rectangle, so we can work out the area of this section by multiplying the width by the height.</p>\n<p>The&nbsp;rectangle is $2$ seconds wide, and $\\var{c1}$ ms<sup>-1</sup> high.</p>\n<p>\\begin{align}<br/>\\text{Area} &amp;= \\text{width} \\times \\text{height}\\\\<br/>&amp;= 2 \\times\\var{c1}\\\\<br/>&amp;=\\simplify{2{c1}}\\text{.}<br/>\\end{align}</p>\n<p>So the distance covered in this two second interval is $\\simplify{2{c1}}$ m.</p>\n<h4>b)</h4>\n<p>The shape made by the line and $x=0$ between $0$&nbsp;and $2$ seconds forms a right-angled triangle with width $2$ and height $\\var{b1}$.</p>\n<p>\\begin{align}<br/>\\text{Area}&amp;= &nbsp;\\frac{1}{2}\\times \\text{width} \\times \\text{height}\\\\<br/>&amp;= \\frac{1}{2} \\times 2 \\times \\var{b1}\\\\<br/>&amp;=\\var{b1} \\text{.}<br/>\\end{align}</p>\n<p>So therefore,the distance covered in this two second interval, and our answer, is $\\simplify{{b1}}$ meters.</p>\n<h4>c)</h4>\n<p>The shape made by the speed curve and $x=0$ between $2$&nbsp;and $4$ seconds forms a trapezium. This can be broken down in to a right angle triangle (let's call this $A$) and a rectangle&nbsp;(we'll call this $B$).</p>\n<p>Triangle $A$ has width $2$ m and height $\\var{c1}-\\var{b1}$ ms<sup>-1</sup>.</p>\n<p>\\begin{align}<br/>A &amp;= &nbsp;\\frac{1}{2}\\times \\text{width} \\times \\text{height}\\\\<br/>&amp;= \\frac{1}{2}\\times2 \\times\\ (\\var{c1}-\\var{b1})\\\\<br/>&amp;= \\var{c1}-\\var{b1}\\\\<br/>&amp;=\\simplify{{c1}-{b1}}\\text{.}<br/>\\end{align}</p>\n<p>We can work out the area of the rectangle $B$&nbsp;by multiplying its width, $2$ seconds, by its height, $\\var{b1}$ ms<sup>-1</sup>:</p>\n<p>\\begin{align}<br/>B &amp;= &nbsp;\\text{width} \\times \\text{height}\\\\<br/>&amp;= 2 \\times(\\var{c1}-\\var{b1})\\\\<br/>&amp;=2 \\times \\simplify{{c1}-{b1}}\\\\<br/>&amp;=\\simplify{2{c1-b1}}\\text{.}<br/>\\end{align}</p>\n<p>We can now work out the whole area under the line by adding these two areas together:</p>\n<p>\\begin{align}<br/>\\text{Area} &amp;= A&nbsp;+ B \\\\<br/>&amp;=\\simplify{{c1}-{b1}} + \\simplify{2{c1-b1}} \\\\<br/>&amp;=\\simplify{2{c1-b1}+{c1}-{b1}} \\text{.}<br/>\\end{align}</p>\n<p>The distance covered in this interval is $\\var{2(c1-b1)+c1-b1}$ m.</p>\n<h4>d)</h4>\n<p>Speed is the distance travelled per unit of time.</p>\n<p>\\begin{align}<br/>\\text{speed} &amp;= \\frac{\\text{distance}}{\\text{time}} \\\\[0.5em]<br/>&amp;=&nbsp;\\frac{\\var{area}}{10} \\\\[0.5em]<br/>&amp;=\\simplify[!fractionNumbers]{{area/10}} \\text{ ms}^{-1}\\text{.}<br/>\\end{align}</p>", "variable_groups": [{"name": "speeds", "variables": ["a1", "b1", "c1", "d1", "z1", "f1"]}, {"name": "acceleration", "variables": ["mab", "mbc", "mcd", "mde", "mef"]}], "statement": "<p>You are part of an elite team analysing a high speed car&nbsp;race. You are given the following graph mapping the speed of one particular car&nbsp;as it drives around a section of the race course. The horizontal axis plots time in seconds&nbsp;whilst the vertical axis maps speed in metres per second ($ms^{-1}$).</p>\n<p style=\"text-align: center;\">{geogebra_applet('cecdYjwp',[[\"a1\",a1],[\"b1\",b1],[\"c1\",c1],[\"d1\",d1],[\"z1\",z1],[\"f1\",f1]])}&nbsp;</p>", "parts": [{"scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "showCorrectAnswer": true, "prompt": "<p>Use the graph to calculate the distance the car travels between $4$ and $6$ seconds.</p>\n<p>Distance travelled $=$ &nbsp;[[0]]metres</p>", "variableReplacements": [], "showFeedbackIcon": true, "marks": 0, "gaps": [{"correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "showFeedbackIcon": true, "marks": 1, "minValue": "c1*2", "scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "maxValue": "c1*2", "mustBeReduced": false, "allowFractions": false, "variableReplacements": [], "correctAnswerStyle": "plain", "showCorrectAnswer": true}]}, {"scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "showCorrectAnswer": true, "prompt": "<p>Use the graph to calculate the distance the car travels between $0$ and $2$ seconds.</p>\n<p>Distance travelled $=$ &nbsp;[[0]]metres</p>", "variableReplacements": [], "showFeedbackIcon": true, "marks": 0, "gaps": [{"correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "showFeedbackIcon": true, "marks": 1, "minValue": "b1", "scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "maxValue": "b1", "mustBeReduced": false, "allowFractions": false, "variableReplacements": [], "correctAnswerStyle": "plain", "showCorrectAnswer": true}]}, {"scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "showCorrectAnswer": true, "prompt": "<p>Use the graph to calculate the distance the car travels between $2$ and $4$ seconds.</p>\n<p>Distance travelled $=$ &nbsp;[[0]]metres</p>", "variableReplacements": [], "showFeedbackIcon": true, "marks": 0, "gaps": [{"correctAnswerFraction": false, "notationStyles": ["plain", "en", "si-en"], "mustBeReducedPC": 0, "showFeedbackIcon": true, "marks": 1, "minValue": "b1+c1", "scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "maxValue": "b1+c1", "mustBeReduced": false, "allowFractions": false, "variableReplacements": [], "correctAnswerStyle": "plain", "showCorrectAnswer": true}]}, {"scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "showCorrectAnswer": true, "prompt": "<p>The car travelled $\\var{area}$ metres over the $10$ second period. Calculate the average speed of the the car over the $10$ seconds in metres per second. Give your answer as a whole number or a decimal to $1$ decimal place.</p>\n<p>Average speed $=$&nbsp;[[0]]&nbsp;ms<sup>-1</sup></p>", "variableReplacements": [], "showFeedbackIcon": true, "marks": 0, "gaps": [{"correctAnswerFraction": false, "variableReplacements": [], "strictPrecision": true, "showCorrectAnswer": true, "mustBeReducedPC": 0, "precision": "1", "showFeedbackIcon": true, "precisionType": "dp", "minValue": "{area/10}", "notationStyles": ["plain", "en", "si-en"], "scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "maxValue": "{area/10}", "mustBeReduced": false, "allowFractions": false, "marks": 1, "precisionPartialCredit": 0, "correctAnswerStyle": "plain", "showPrecisionHint": true, "precisionMessage": "You have not given your answer to the correct precision."}]}], "tags": ["average speed", "calculating distance", "constant accelerations", "distance", "Distance", "graphs", "speed graph", "taxonomy"], "preamble": {"css": "", "js": ""}, "functions": {}, "variables": {"d2farea": {"description": "", "group": "Ungrouped variables", "definition": "2*z1+d1+f1", "name": "d2farea", "templateType": "anything"}, "c1": {"description": "", "group": "speeds", "definition": "random(8,10,12,14)+b1", "name": "c1", "templateType": "anything"}, "a1": {"description": "", "group": "speeds", "definition": "0\n", "name": "a1", "templateType": "anything"}, "d1": {"description": "", "group": "speeds", "definition": "c1", "name": "d1", "templateType": "anything"}, "b1": {"description": "", "group": "speeds", "definition": "random(6,8,10)+a1\n", "name": "b1", "templateType": "anything"}, "area": {"description": "", "group": "Ungrouped variables", "definition": "d2farea+c1*2+b1+c1+b1", "name": "area", "templateType": "anything"}, "z1": {"description": "", "group": "speeds", "definition": "c1-random(8,10,12)", "name": "z1", "templateType": "anything"}, "mbc": {"description": "", "group": "acceleration", "definition": "(c1-b1)/2", "name": "mbc", "templateType": "anything"}, "mde": {"description": "", "group": "acceleration", "definition": "(z1-d1)/2", "name": "mde", "templateType": "anything"}, "mab": {"description": "", "group": "acceleration", "definition": "(b1-a1)/2", "name": "mab", "templateType": "anything"}, "mef": {"description": "", "group": "acceleration", "definition": "(f1-z1)/2", "name": "mef", "templateType": "anything"}, "f1": {"description": "", "group": "speeds", "definition": "2", "name": "f1", "templateType": "anything"}, "mcd": {"description": "", "group": "acceleration", "definition": "(d1-c1)/2", "name": "mcd", "templateType": "anything"}}, "variablesTest": {"maxRuns": 100, "condition": ""}}, {"name": "Creating Frequency Tables", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Elliott Fletcher", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1591/"}], "rulesets": {}, "functions": {"tally": {"parameters": [["n", "number"]], "language": "javascript", "type": "string", "definition": "var s = ''\n// Add strikethrough if n>=5\n// For simplicity, I have not handled the case where n reaches 10, which is unlikely.\nif(n>=5){\n s = '<strike>||||</strike> ';\n n = n-5;\n}\n// Tally for each n\nfor (i=1; i <= n; i++) { \n  s+= '|';\n}\nreturn '<b>'+s+'</b>';"}}, "ungrouped_variables": ["data", "frequencies", "tallies"], "metadata": {"description": "<p>Present some given data in a frequency table.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "variable_groups": [], "advice": "<p></p>\n<p>Frequency is the number of times that an event occurs (in this case,&nbsp;obtaining a certain score) within a particular experiment&nbsp;(in this case, the&nbsp;exam).</p>\n<p>We are given enough data that keeping a mental count of the frequencies is difficult:</p>\n<table width=\"1414\" height=\"68\" border=\"-\" style=\"height: 76px; margin-left: auto; margin-right: auto;\">\n<tbody>\n<tr>\n<td style=\"width: 125px; text-align: center;\">$\\var{data[0]}$</td>\n<td style=\"width: 125px; text-align: center;\">$\\var{data[1]}$</td>\n<td style=\"width: 125px; text-align: center;\">$\\var{data[2]}$</td>\n<td style=\"width: 125px; text-align: center;\">$\\var{data[3]}$</td>\n<td style=\"width: 125px; text-align: center;\">$\\var{data[4]}$</td>\n<td style=\"width: 125px; text-align: center;\">$\\var{data[5]}$</td>\n<td style=\"width: 125px; text-align: center;\">$\\var{data[6]}$</td>\n<td style=\"width: 126px; text-align: center;\">$\\var{data[7]}$</td>\n<td style=\"width: 126px; text-align: center;\">$\\var{data[8]}$</td>\n<td style=\"width: 126px; text-align: center;\">$\\var{data[9]}$</td>\n</tr>\n<tr>\n<td style=\"width: 125px; text-align: center;\">$\\var{data[10]}$</td>\n<td style=\"width: 125px; text-align: center;\">$\\var{data[11]}$</td>\n<td style=\"width: 125px; text-align: center;\">$\\var{data[12]}$</td>\n<td style=\"width: 125px; text-align: center;\">$\\var{data[13]}$</td>\n<td style=\"width: 125px; text-align: center;\">$\\var{data[14]}$</td>\n<td style=\"width: 125px; text-align: center;\">$\\var{data[15]}$</td>\n<td style=\"width: 125px; text-align: center;\">$\\var{data[16]}$</td>\n<td style=\"width: 126px; text-align: center;\">$\\var{data[17]}$</td>\n<td style=\"width: 126px; text-align: center;\">$\\var{data[18]}$</td>\n<td style=\"width: 126px; text-align: center;\">$\\var{data[19]}$</td>\n</tr>\n</tbody>\n</table>\n<p style=\"text-align: left;\">Therefore, a better way to approach this problem would be to add an&nbsp;extra column&nbsp;to the frequency table,&nbsp;as illustrated below,&nbsp;to tally the number of&nbsp;students with each score.&nbsp;The&nbsp;number of tally marks for each score can then be read off and insterted into the&nbsp;frequency column.</p>\n<table height=\"314\" style=\"height: 430px; margin-right: auto; margin-left: auto; width: 398.5px;\" border=\"-\"><caption></caption>\n<tbody>\n<tr>\n<td style=\"width: 119px; text-align: center;\">Score</td>\n<td style=\"width: 116px; text-align: center;\">Tally</td>\n<td style=\"width: 114.5px; text-align: center;\">Frequency</td>\n</tr>\n<tr>\n<td style=\"width: 119px; text-align: center;\">$0$</td>\n<td style=\"width: 116px;\">{tallies[0]}</td>\n<td style=\"width: 114.5px;\">$\\var{frequencies[0]}$</td>\n</tr>\n<tr>\n<td style=\"width: 119px; text-align: center;\">$1$</td>\n<td style=\"width: 116px;\">{tallies[1]}<span style=\"text-decoration: line-through;\"></span></td>\n<td style=\"width: 114.5px;\">$\\var{frequencies[1]}$</td>\n</tr>\n<tr>\n<td style=\"width: 119px; text-align: center;\">$2$</td>\n<td style=\"width: 116px;\">{tallies[2]}</td>\n<td style=\"width: 114.5px;\">$\\var{frequencies[2]}$</td>\n</tr>\n<tr>\n<td style=\"width: 119px; text-align: center;\">$3$</td>\n<td style=\"width: 116px;\">{tallies[3]}</td>\n<td style=\"width: 114.5px;\">$\\var{frequencies[3]}$</td>\n</tr>\n<tr>\n<td style=\"width: 119px; text-align: center;\">$4$</td>\n<td style=\"width: 116px;\">{tallies[4]}</td>\n<td style=\"width: 114.5px;\">$\\var{frequencies[4]}$</td>\n</tr>\n<tr>\n<td style=\"width: 119px; text-align: center;\">$5$</td>\n<td style=\"width: 116px;\">{tallies[5]}</td>\n<td style=\"width: 114.5px;\">$\\var{frequencies[5]}$</td>\n</tr>\n<tr>\n<td style=\"width: 119px; text-align: center;\">$6$</td>\n<td style=\"width: 116px;\">{tallies[6]}</td>\n<td style=\"width: 114.5px;\">$\\var{frequencies[6]}$</td>\n</tr>\n<tr>\n<td style=\"width: 119px; text-align: center;\">$7$</td>\n<td style=\"width: 116px;\">{tallies[7]}</td>\n<td style=\"width: 114.5px;\">$\\var{frequencies[7]}$</td>\n</tr>\n<tr>\n<td style=\"width: 119px; text-align: center;\">$8$</td>\n<td style=\"width: 116px;\">{tallies[8]}</td>\n<td style=\"width: 114.5px;\">$\\var{frequencies[8]}$</td>\n</tr>\n<tr>\n<td style=\"width: 119px; text-align: center;\">$9$</td>\n<td style=\"width: 116px;\">{tallies[9]}</td>\n<td style=\"width: 114.5px;\">$\\var{frequencies[9]}$</td>\n</tr>\n<tr>\n<td style=\"width: 119px; text-align: center;\">$10$</td>\n<td style=\"width: 116px;\">{tallies[10]}</td>\n<td style=\"width: 114.5px;\">$\\var{frequencies[10]}$</td>\n</tr>\n</tbody>\n</table>\n<p><br/><br/></p>", "statement": "<p>A maths test in a Year 7 class of $20$ students was scored out of $10$. The marks awarded to the students were as follows:</p>\n<table width=\"1402\" height=\"68\" border=\"-\" style=\"height: 71px; margin-left: auto; margin-right: auto;\">\n<tbody>\n<tr>\n<td style=\"width: 125px; text-align: center;\">$\\var{data[0]}$</td>\n<td style=\"width: 125px; text-align: center;\">$\\var{data[1]}$</td>\n<td style=\"width: 125px; text-align: center;\">$\\var{data[2]}$</td>\n<td style=\"width: 125px; text-align: center;\">$\\var{data[3]}$</td>\n<td style=\"width: 125px; text-align: center;\">$\\var{data[4]}$</td>\n<td style=\"width: 125px; text-align: center;\">$\\var{data[5]}$</td>\n<td style=\"width: 125px; text-align: center;\">$\\var{data[6]}$</td>\n<td style=\"width: 125px; text-align: center;\">$\\var{data[7]}$</td>\n<td style=\"width: 125px; text-align: center;\">$\\var{data[8]}$</td>\n<td style=\"width: 125px; text-align: center;\">$\\var{data[9]}$</td>\n</tr>\n<tr>\n<td style=\"width: 125px; text-align: center;\">$\\var{data[10]}$</td>\n<td style=\"width: 125px; text-align: center;\">$\\var{data[11]}$</td>\n<td style=\"width: 125px; text-align: center;\">$\\var{data[12]}$</td>\n<td style=\"width: 125px; text-align: center;\">$\\var{data[13]}$</td>\n<td style=\"width: 125px; text-align: center;\">$\\var{data[14]}$</td>\n<td style=\"width: 125px; text-align: center;\">$\\var{data[15]}$</td>\n<td style=\"width: 125px; text-align: center;\">$\\var{data[16]}$</td>\n<td style=\"width: 125px; text-align: center;\">$\\var{data[17]}$</td>\n<td style=\"width: 125px; text-align: center;\">$\\var{data[18]}$</td>\n<td style=\"width: 125px; text-align: center;\">$\\var{data[19]}$</td>\n</tr>\n</tbody>\n</table>", "preamble": {"css": "", "js": ""}, "tags": ["Frequency", "Frequency Table", "frequency table", "Frequency table", "taxonomy"], "parts": [{"variableReplacementStrategy": "originalfirst", "prompt": "<p></p>\n<p style=\"text-align: left;\">Complete the frequency table for this data.</p>\n<p style=\"text-align: left;\"></p>\n<table width=\"333\" height=\"375\" style=\"border-color: #000000; height: 375px; margin-right: auto; margin-left: auto;\" border=\"-\">\n<tbody>\n<tr>\n<td style=\"width: 122.41px; text-align: center;\">Score</td>\n<td style=\"width: 177.59px; text-align: center;\">Frequency</td>\n</tr>\n<tr>\n<td style=\"width: 122.41px; text-align: center;\">$0$</td>\n<td style=\"width: 122.59px; padding-left: 60px;\">[[0]]</td>\n</tr>\n<tr>\n<td style=\"width: 122.41px; text-align: center;\">$1$</td>\n<td style=\"width: 122.59px; padding-left: 60px;\">[[1]]</td>\n</tr>\n<tr>\n<td style=\"width: 122.41px; text-align: center;\">$2$</td>\n<td style=\"width: 122.59px; padding-left: 60px;\">[[2]]</td>\n</tr>\n<tr>\n<td style=\"width: 122.41px; text-align: center;\">$3$</td>\n<td style=\"width: 122.59px; padding-left: 60px;\">[[3]]</td>\n</tr>\n<tr>\n<td style=\"width: 122.41px; text-align: center;\">$4$</td>\n<td style=\"width: 122.59px; padding-left: 60px;\">[[4]]</td>\n</tr>\n<tr>\n<td style=\"width: 122.41px; text-align: center;\">$5$</td>\n<td style=\"width: 122.59px; padding-left: 60px;\">[[5]]</td>\n</tr>\n<tr>\n<td style=\"width: 122.41px; text-align: center;\">$6$</td>\n<td style=\"width: 122.59px; padding-left: 60px;\">[[6]]</td>\n</tr>\n<tr>\n<td style=\"width: 122.41px; text-align: center;\">$7$</td>\n<td style=\"width: 122.59px; padding-left: 60px;\">[[7]]</td>\n</tr>\n<tr>\n<td style=\"width: 122.41px; text-align: center;\">$8$</td>\n<td style=\"width: 122.59px; padding-left: 60px;\">[[8]]</td>\n</tr>\n<tr>\n<td style=\"width: 122.41px; text-align: center;\">$9$</td>\n<td style=\"width: 122.59px; padding-left: 60px;\">[[9]]</td>\n</tr>\n<tr>\n<td style=\"width: 122.41px; text-align: center;\">$10$</td>\n<td style=\"width: 122.59px; padding-left: 60px;\">[[10]]</td>\n</tr>\n</tbody>\n</table>\n<p></p>", "gaps": [{"mustBeReducedPC": 0, "marks": 1, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "type": "numberentry", "correctAnswerFraction": false, "maxValue": "{frequencies[0]}", "allowFractions": false, "minValue": "{frequencies[0]}", "mustBeReduced": false, "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "scripts": {}}, {"mustBeReducedPC": 0, "marks": 1, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "type": "numberentry", "correctAnswerFraction": false, "maxValue": "{frequencies[1]}", "allowFractions": false, "minValue": "{frequencies[1]}", "mustBeReduced": false, "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "scripts": {}}, {"mustBeReducedPC": 0, "marks": 1, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "type": "numberentry", "correctAnswerFraction": false, "maxValue": "{frequencies[2]}", "allowFractions": false, "minValue": "{frequencies[2]}", "mustBeReduced": false, "variableReplacements": [], "showFeedbackIcon": true, 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"variableReplacementStrategy": "originalfirst", "type": "numberentry", "correctAnswerFraction": false, "maxValue": "{frequencies[5]}", "allowFractions": false, "minValue": "{frequencies[5]}", "mustBeReduced": false, "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "scripts": {}}, {"mustBeReducedPC": 0, "marks": 1, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "type": "numberentry", "correctAnswerFraction": false, "maxValue": "{frequencies[6]}", "allowFractions": false, "minValue": "{frequencies[6]}", "mustBeReduced": false, "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "scripts": {}}, {"mustBeReducedPC": 0, "marks": 1, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "type": "numberentry", "correctAnswerFraction": false, "maxValue": "{frequencies[7]}", "allowFractions": false, "minValue": "{frequencies[7]}", "mustBeReduced": false, "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "scripts": {}}, {"mustBeReducedPC": 0, "marks": 1, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "type": "numberentry", "correctAnswerFraction": false, "maxValue": "{frequencies[8]}", "allowFractions": false, "minValue": "{frequencies[8]}", "mustBeReduced": false, "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "scripts": {}}, {"mustBeReducedPC": 0, "marks": 1, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "type": "numberentry", "correctAnswerFraction": false, "maxValue": "{frequencies[9]}", "allowFractions": false, "minValue": "{frequencies[9]}", "mustBeReduced": false, "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "scripts": {}}, {"mustBeReducedPC": 0, "marks": 1, "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "type": "numberentry", "correctAnswerFraction": false, "maxValue": "{frequencies[10]}", "allowFractions": false, "minValue": "{frequencies[10]}", "mustBeReduced": false, "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "scripts": {}}], "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "type": "gapfill", "marks": 0, "showCorrectAnswer": true}], "variables": {"data": {"name": "data", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "repeat(min(max(precround(normalsample(6,2.5),0),0),10),20)"}, "tallies": {"name": "tallies", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "map(tally(frequencies[x]),x,0..10)"}, "frequencies": {"name": "frequencies", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "map(\nlen(filter(x=j,x,data)),\nj,0..10)"}}, "variablesTest": {"maxRuns": 100, "condition": ""}}, {"name": "Complete a frequency table and find the measures of central tendency", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Chris Graham", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/369/"}, {"name": "Stanislav Duris", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1590/"}], "tags": ["Frequency Table", "frequency table", "Frequency table", "taxonomy"], "metadata": {"description": "<p>Given a table of data, calculate the mean, mode and median, and complete a frequency table.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>30 random students were asked about the number of siblings they have. These are their responses:</p>\n<table border=\"1\" cellspacing=\"10\" cellpadding=\"10\">\n<tbody>\n<tr>\n<td>$\\var{a[0]}$</td>\n<td>$\\var{a[1]}$</td>\n<td>$\\var{a[2]}$</td>\n<td>$\\var{a[3]}$</td>\n<td>$\\var{a[4]}$</td>\n<td>$\\var{a[5]}$</td>\n<td>$\\var{a[6]}$</td>\n<td>$\\var{a[7]}$</td>\n<td>$\\var{a[8]}$</td>\n<td>$\\var{a[9]}$</td>\n</tr>\n<tr>\n<td>$\\var{a[10]}$</td>\n<td>$\\var{a[11]}$</td>\n<td>$\\var{a[12]}$</td>\n<td>$\\var{a[13]}$</td>\n<td>$\\var{a[14]}$</td>\n<td>$\\var{a[15]}$</td>\n<td>$\\var{a[16]}$</td>\n<td>$\\var{a[17]}$</td>\n<td>$\\var{a[18]}$</td>\n<td>$\\var{a[19]}$</td>\n</tr>\n<tr>\n<td>$\\var{a[20]}$</td>\n<td>$\\var{a[21]}$</td>\n<td>$\\var{a[22]}$</td>\n<td>$\\var{a[23]}$</td>\n<td>$\\var{a[24]}$</td>\n<td>$\\var{a[25]}$</td>\n<td>$\\var{a[26]}$</td>\n<td>$\\var{a[27]}$</td>\n<td>$\\var{a[28]}$</td>\n<td>$\\var{a[29]}$</td>\n</tr>\n</tbody>\n</table>\n<p></p>", "advice": "<h4>a)</h4>\n<p>Organising the data in a frequency table helps to make mistakes less likely when calculating statistics from our data, summarising the responses all in one place with fewer numbers.</p>\n<p>Each row of the frequency column gives&nbsp;the number of students with the corresponding number of siblings.</p>\n<table border=\"1\">\n<tbody>\n<tr>\n<th>Number of siblings</th>\n<th>Frequency</th>\n</tr>\n<tr>\n<td style=\"text-align: left;\">$0$</td>\n<td style=\"text-align: left;\">$\\var{freq[0]}$</td>\n</tr>\n<tr>\n<td style=\"text-align: left;\">$1$</td>\n<td style=\"text-align: left;\">$\\var{freq[1]}$</td>\n</tr>\n<tr>\n<td style=\"text-align: left;\">$2$</td>\n<td style=\"text-align: left;\">$\\var{freq[2]}$</td>\n</tr>\n<tr>\n<td style=\"text-align: left;\">$3$</td>\n<td style=\"text-align: left;\">$\\var{freq[3]}$</td>\n</tr>\n<tr>\n<td style=\"text-align: left;\">$4$</td>\n<td style=\"text-align: left;\">$\\var{freq[4]}$</td>\n</tr>\n<tr>\n<td style=\"text-align: left;\">$5$</td>\n<td style=\"text-align: left;\">$\\var{freq[5]}$</td>\n</tr>\n<tr>\n<td style=\"text-align: left;\">$6$</td>\n<td style=\"text-align: left;\">$\\var{freq[6]}$</td>\n</tr>\n<tr>\n<td style=\"text-align: left;\">Total</td>\n<td style=\"text-align: left;\">$30$</td>\n</tr>\n</tbody>\n</table>\n<p>Always remember to check whether your frequency column adds up to the total (here, it is $30$) to make sure you have not left out any responses.</p>\n<h4>b)</h4>\n<h4>Mean</h4>\n<p>The mean number of siblings is the total number of siblings, $\\sum x$, divided by the number of students in the sample, $n$.</p>\n<p>\\begin{align} &nbsp;<br/>\\sum x &amp;= 0 \\times \\var{freq[0]} +&nbsp;1 \\times \\var{freq[1]} +&nbsp;2 \\times \\var{freq[2]} +&nbsp;3 \\times \\var{freq[3]} +&nbsp;4 \\times \\var{freq[4]} +&nbsp;5 \\times \\var{freq[5]} +&nbsp;6 \\times \\var{freq[6]}<br/> \\\\<br/>&amp;=&nbsp;0 + \\var{1*freq[1]} + \\var{2*freq[2]}&nbsp;+ \\var{3*freq[3]}&nbsp;+ \\var{4*freq[4]}&nbsp;+ \\var{5*freq[5]}&nbsp;+ \\var{6*freq[6]}&nbsp;\\\\&amp;= \\var{sum(a)} \\text{.}<br/>\\end{align}</p>\n<p>The total number of students $n$ is $30$.</p>\n<p>Therefore the mean is</p>\n<p><span face=\"Courier New\">\\begin{align} <br/>\\bar{x} &amp;= \\frac{\\sum x}{n}&nbsp;\\\\<br/>&amp;= \\frac{\\var{sum(a)}}{30}&nbsp;\\\\<br/>&amp;= \\var{mean} \\text{.} <br/>\\end{align}</span></p>\n<p><span data-jme-visible=\"mean &lt;&gt; precround(mean, 2)\" face=\"Courier New\">Rounding the answer to 2 decimal places, we get&nbsp;$\\var{precround(mean, 2)}$.</span></p>\n<h4>Mode</h4>\n<p>The mode is the value with the highest frequency. Here, the mode is $\\var{mode}$ sibling<span data-jme-visible=\"mode &lt;&gt; 1\">s</span>, with frequency $\\var{freq[mode]}$.</p>\n<h4>Median</h4>\n<p>The median is the \"middle\" value in the sample, when&nbsp;arranged in numerical order.</p>\n<p>Since $n = 30$, we have two middle values in this data (15<sup>th</sup> and 16<sup>th</sup> place). We can count from the top of the table until we locate rows where these middle values lie, as the numbers in the table are already sorted by order.</p>\n<p><span data-jme-visible=\"asa[14] = asa[15]\">Here, both $15$<sup>th</sup> and $16$<sup>th</sup> value lie in the row $\\var{asa[14]}$.</span><span data-jme-visible=\"asa[14] &lt;&gt; asa[15]\">Here, the $15$<sup>th</sup> value lies in the row $\\var{asa[14]}$ while the $16$<sup>th</sup> value lies in the row $\\var{asa[15]}$.</span></p>\n<p><span data-jme-visible=\"asa[14] = asa[15]\">As $15$<sup>th</sup> value $= 16$<sup>th</sup> value $= \\var{asa[14]}$, the median is $\\var{asa[14]}$.</span><span data-jme-visible=\"asa[14] &lt;&gt; asa[15]\">As $15$<sup>th</sup> value $= \\var{asa[14]}$ and $16$<sup>th</sup> value $= \\var{asa[15]}$, we need to find their mean.</span></p>\n<p><span data-jme-visible=\"asa[14] &lt;&gt; asa[15]\">\\[ \\displaystyle \\begin{align} \\frac{\\var{asa[14]} + \\var{asa[15]}}{2} &amp;= &nbsp;\\frac{\\var{asa[14] + asa[15]}}{2} \\\\&amp;= \\var{median} \\text{.}&nbsp;\\end{align}\\]</span></p>\n<p><span data-jme-visible=\"asa[14] &lt;&gt; asa[15]\">This is the median for this data.</span></p>\n<p></p>", "rulesets": {}, "variables": {"m": {"name": "m", "group": "Final data", "definition": "mode(a)", "description": "", "templateType": "anything"}, "a2": {"name": "a2", "group": "Ungrouped variables", "definition": "shuffle(repeat(random(0..1), 13) + 0 + 2 + 2 + repeat(random(2..3), 10) + repeat(random(4..5), 3) + random(0..6))", "description": "", "templateType": "anything"}, "a1": {"name": "a1", "group": "Ungrouped variables", "definition": "shuffle(repeat(random(0..1), 13) + 0 + 2 + 2 + repeat(random(2..3), 10) + repeat(random(4..5), 3) + random(0..6))", "description": "", "templateType": "anything"}, "modea1": {"name": "modea1", "group": "Ungrouped variables", "definition": "mode(a1)", "description": "", "templateType": "anything"}, "mode": {"name": "mode", "group": "Final data", "definition": "m[0]", "description": "", "templateType": "anything"}, "mean": {"name": "mean", "group": "Final data", "definition": "mean(a)", "description": "", "templateType": "anything"}, "modea2": {"name": "modea2", "group": "Ungrouped variables", "definition": "mode(a2)", "description": "", "templateType": "anything"}, "a3": {"name": "a3", "group": "Ungrouped variables", "definition": "shuffle(repeat(0, 7) + repeat(1, 10) + repeat(2, 5) + repeat(3, 4) + repeat(4, 2) + repeat(5,1) + repeat(6,1))", "description": "", "templateType": "anything"}, "freq": {"name": "freq", "group": "Final data", "definition": "map(\nlen(filter(x=j,x,a)),\nj, 0..6)", "description": "", "templateType": "anything"}, "median": {"name": "median", "group": "Final data", "definition": "median(a)", "description": "", "templateType": "anything"}, "a": {"name": "a", "group": "Final data", "definition": "if(len(modea1) = 1, a1, if(len(modea2) = 1, a2, a3))", "description": "", "templateType": "anything"}, "modea3": {"name": "modea3", "group": "Ungrouped variables", "definition": "mode(a3)", "description": "", "templateType": "anything"}, "asa": {"name": "asa", "group": "Final data", "definition": "sort(a)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": "1000"}, "ungrouped_variables": ["a1", "modea1", "a2", "modea2", "a3", "modea3"], "variable_groups": [{"name": "Final data", "variables": ["a", "mean", "median", "m", "mode", "freq", "asa"]}], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Complete the following frequency table:</p>\n<table border=\"1\">\n<tbody>\n<tr>\n<th>Number of siblings</th>\n<th>Frequency</th>\n</tr>\n<tr>\n<td style=\"text-align: left;\">$0$</td>\n<td style=\"text-align: left;\">[[0]]</td>\n</tr>\n<tr>\n<td style=\"text-align: left;\">$1$</td>\n<td style=\"text-align: left;\">[[1]]</td>\n</tr>\n<tr>\n<td style=\"text-align: left;\">$2$</td>\n<td style=\"text-align: left;\">[[2]]</td>\n</tr>\n<tr>\n<td style=\"text-align: left;\">$3$</td>\n<td style=\"text-align: left;\">[[3]]</td>\n</tr>\n<tr>\n<td style=\"text-align: left;\">$4$</td>\n<td style=\"text-align: left;\">[[4]]</td>\n</tr>\n<tr>\n<td style=\"text-align: left;\">$5$</td>\n<td style=\"text-align: left;\">[[5]]</td>\n</tr>\n<tr>\n<td style=\"text-align: left;\">$6$</td>\n<td style=\"text-align: left;\">[[6]]</td>\n</tr>\n<tr>\n<td style=\"text-align: left;\">Total</td>\n<td style=\"text-align: left;\">$30$</td>\n</tr>\n</tbody>\n</table>\n<p></p>", "gaps": [{"type": "numberentry", "useCustomName": 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