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5 minutes remaining

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Click on Pause if you wish to leave and resume the same attempt at a later stage.  All completed work is saved. 

\n

When you have finally finished click on End Exam.

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Calculate the cumulative frequecy distribution and the relative cumulative frequency distribution.

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
xCumulative Frequency Distribution\n

Relative Cumulative Frequency Distribution

\n

Enter answer in decimal form (not percentage)

\n

(correct to 2 decimal places)

\n
Less than 50[[0]][[1]]
Less than 60[[2]][[3]]
Less than 70[[4]][[5]]
Less than 80[[6]][[7]]
Less than 90[[8]][[9]]
Less than 100[[10]][[11]]
\n

\n

 

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true, "scripts": {}, "marks": "0.5", "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "({a}+{b}+{c}+{d})/{tot}", "strictPrecision": false, "minValue": "({a}+{b}+{c}+{d})/{tot}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": "0.5", "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "({a}+{b}+{c}+{d}+{f})", "minValue": "({a}+{b}+{c}+{d}+{f})", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": "0.5", "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "({a}+{b}+{c}+{d}+{f})/{tot}", "strictPrecision": false, "minValue": "({a}+{b}+{c}+{d}+{f})/{tot}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "2", "scripts": {}, "marks": "0.5", "type": "numberentry", "showPrecisionHint": false}, {"allowFractions": false, "variableReplacements": [], "maxValue": "{a}+{b}+{c}+{d}+{f}+{g}", "minValue": "{a}+{b}+{c}+{d}+{f}+{g}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": "0.5", "type": "numberentry", "showPrecisionHint": false}, {"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "({a}+{b}+{c}+{d}+{f}+{g})/{tot}", 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The table below shows the frequency distribution for {thing}.

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
xf
40 but less than 50{a}
50 but less than 60{b}
60 but less than 70{c}
70 but less than 80{d}
80 but less than 90{f}
90 but less than 100{g}
\n

 

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Cumulative Frequency Distribution

\n

rebelmaths

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Given random set of data (between 13 and 23 numbers all less than 100), find their stem-and-leaf plot.

\n

rebelmaths

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STEMLEAF
$\\var{v}$[[0]][[1]][[2]][[3]][[4]]
$\\var{v+1}$[[5]][[6]][[7]][[8]][[9]]
$\\var{v+2}$[[10]][[11]][[12]][[13]][[14]]
$\\var{v+3}$[[15]][[16]][[17]][[18]][[19]]
$\\var{v+4}$[[20]][[21]][[22]][[23]][[24]]
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"maxValue": "{u[4][0]}", "showCorrectAnswer": true, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "scripts": {}, "variableReplacements": [], "marks": 0.2}, {"allowFractions": false, "minValue": "{u[4][1]}", "showPrecisionHint": false, "maxValue": "{u[4][1]}", "showCorrectAnswer": true, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "scripts": {}, "variableReplacements": [], "marks": 0.2}, {"allowFractions": false, "minValue": "{u[4][2]}", "showPrecisionHint": false, "maxValue": "{u[4][2]}", "showCorrectAnswer": true, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "scripts": {}, "variableReplacements": [], "marks": 0.2}, {"allowFractions": false, "minValue": "{u[4][3]}", "showPrecisionHint": false, "maxValue": "{u[4][3]}", "showCorrectAnswer": true, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "scripts": {}, "variableReplacements": [], "marks": 0.2}, {"allowFractions": false, "minValue": "{u[4][4]}", "showPrecisionHint": false, "maxValue": "{u[4][4]}", "showCorrectAnswer": true, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "scripts": {}, "variableReplacements": [], "marks": 0.2}], "type": "gapfill", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "variableReplacements": [], "marks": 0}], "statement": "\n

Construct a stem-and-leaf plot for the following data. Input all numbers into the fields below.

\n

{table([ss],[])}

\n

 NOTE: All 25 fields have to be filled in. Input -1 if there is no number in a field.

\n

 

\n

 

\n \n", "question_groups": [{"pickingStrategy": "all-ordered", "name": "", "questions": [], "pickQuestions": 0}], "variables": {"darr1": {"description": "", "name": "darr1", "definition": "map(['$'+(v+y)+'$'+ ':']+arr1[y],y,0..4)", "group": "Ungrouped variables", "templateType": "anything"}, "ss": {"description": "", "name": "ss", "definition": "shuffle(s)", "group": "Ungrouped variables", "templateType": "anything"}, "v": {"description": "", "name": "v", "definition": "random(0..4)", "group": "Ungrouped variables", "templateType": "anything"}, "s": {"description": "", "name": "s", "definition": "flattenint(arr)", "group": "Ungrouped variables", "templateType": "anything"}, "arr1": {"description": "", "name": "arr1", "definition": "map(map(arr[y][p]-10*(y+v),p,0..r[y]-1),y,0..4)", "group": "Ungrouped variables", "templateType": "anything"}, "u": {"description": "", "name": "u", "definition": "map(map(if(pOrdering the data gives:

\n

{table([s],[])}

\n

Splitting into the groups of 10s gives

\n

{table(arr,[])}

\n

Then putting this into stem-and-leaf plot gives

\n

{table(darr1,['STEM'])}

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Check you're using the correct axis.

", "rulesets": {}, "parts": [{"prompt": "

How many people waited less than 20 minutes?

", "allowFractions": false, "variableReplacements": [], "maxValue": "10", "minValue": "10", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"prompt": "

Give an estimate for the number of people who waited between 20 and 40 minutes.

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The cumulative frequency diagram gives information about the time, in minutes, 50 people were kept waiting at hospital.

\n

", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {}, "metadata": {"description": "

rebelmaths

", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Qualitative v Quantative", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}], "functions": {}, "ungrouped_variables": ["quant1", "quant2", "qual2", "cind", "qual1", "m", "ch1", "ch2", "ch3", "quant", "ind", "ind1", "qual"], "tags": ["qualitative variables", "quantitative variables", "random variables", "rebel", "Rebel", "REBEL", "rebelmaths", "statistics"], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"maxAnswers": 0, "shuffleChoices": true, "matrix": "m", "shuffleAnswers": true, "minAnswers": 0, "variableReplacements": [], "answers": ["

Qualitative (Categorical)

", "

Quantitative (Numerical)

"], "warningType": "none", "variableReplacementStrategy": "originalfirst", "maxMarks": 0, "showCorrectAnswer": true, "scripts": {}, "marks": 0, "choices": ["{ch1}", "{ch2}", "{ch3}"], "type": "m_n_x", "displayType": "radiogroup", "minMarks": 0, "layout": {"expression": "", "type": "all"}}], "statement": "

State whether the following variables are Qualitative (Categorical) or Quantitative(numerical). 

\n

Note that you will be deducted one mark for every wrong choice. However the minimum mark is 0.

", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"quant1": {"definition": "[\"The number of orders received by a catering company\",\"The height of students taking Statistics courses at Newcastle this year\", \"Your quarterly gas bill\", \"The time spent on hold at a credit call centre\",\"The average shipping time for orders placed with a TV shopping channel\",\"The annual electricity bill for a large UK Supermarket\"]", "templateType": "anything", "group": "Ungrouped variables", "name": "quant1", "description": ""}, "quant2": {"definition": "[\"The number of people requiring a special in-flight meal\",\"The average volume of bottles of wine imported from South America\",\"Salaries of Newcastle University graduates six months after graduation\",\"The distance travelled by taxis for a particular cab firm every day\",\"Total annual sales for a large American departmental store\",\"The total cost of a student's text books for this semester\"]", "templateType": "anything", "group": "Ungrouped variables", "name": "quant2", "description": ""}, "qual2": {"definition": "[\"Ice cream flavour preferred by children\",\"Brand of sportswear preferred by athletes\",\"Favourite type of film by UK cinema-goers\",\"Mobile phone price-plan\",\"Shape of swimming pools in local authority-run leisure centres\"]", "templateType": "anything", "group": "Ungrouped variables", "name": "qual2", "description": ""}, "cind": {"definition": "-1*ind1", "templateType": "anything", "group": "Ungrouped variables", "name": "cind", "description": ""}, "qual1": {"definition": "[\"Types of PC used by small businesses in the north-east\",\"Marital status of questionnaire respondents\",\"Month of the year in which small shops record their highest sales\",\"Type of tenure for those in the licensed trade business\",\"Subjects studied at A level by students in this class\"]", "templateType": "anything", "group": "Ungrouped variables", "name": "qual1", "description": ""}, "m": {"definition": "transpose(matrix(list(cind),list(ind1)))", "templateType": "anything", "group": "Ungrouped variables", "name": "m", "description": ""}, "ch1": {"definition": "switch(ind[0]=0,random(qual),random(quant))", "templateType": "anything", "group": "Ungrouped variables", "name": "ch1", "description": ""}, "ch2": {"definition": "switch(ind[1]=0,random(qual except ch1),random(quant except ch1))", "templateType": "anything", "group": "Ungrouped variables", "name": "ch2", "description": ""}, "ch3": {"definition": "switch(ind[2]=0,random(qual except [ch1,ch2]),random(quant except [ch1,ch2]))", "templateType": "anything", "group": "Ungrouped variables", "name": "ch3", "description": ""}, "quant": {"definition": "quant1+quant2", "templateType": "anything", "group": "Ungrouped variables", "name": "quant", "description": ""}, "ind": {"definition": "random([[0,0,0],[1,0,0],[0,1,0],[0,0,1],[0,1,1],[1,0,1],[1,1,0],[1,1,1]])", "templateType": "anything", "group": "Ungrouped variables", "name": "ind", "description": ""}, "ind1": {"definition": "2*vector(ind)-vector(1,1,1)", "templateType": "anything", "group": "Ungrouped variables", "name": "ind1", "description": ""}, "qual": {"definition": "qual1+qual2", "templateType": "anything", "group": "Ungrouped variables", "name": "qual", "description": ""}}, "metadata": {"description": "

Choosing whether given random variables are qualitiative or quantitative.

\n

rebelmaths

", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Summation notation ", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}], "tags": ["REBEL", "rebel", "Rebel", "rebelmaths", "summation"], "metadata": {"description": "

rebelmaths

", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "

The following table lists five pairs of $x$ and $f$ values.

\n\n\n\n\n\n\n\n\n\n\n\n
$\\mathbf{x}${x1}{x2}{x3}{x4}{x5}
$\\mathbf{f} ${f1}{f2}{f3}{f4}{f5}
", "advice": "", "rulesets": {}, "variables": {"f1": {"name": "f1", "group": "Ungrouped variables", "definition": "random(2 .. 20#1)", "description": "", "templateType": "randrange"}, "f2": {"name": "f2", "group": "Ungrouped variables", "definition": "random(5 .. 20#1)", "description": "", "templateType": "randrange"}, "f3": {"name": "f3", "group": "Ungrouped variables", "definition": "random(5 .. 20#1)", "description": "", "templateType": "randrange"}, "f4": {"name": "f4", "group": "Ungrouped variables", "definition": "random(7 .. 10#1)", "description": "", "templateType": "randrange"}, "f5": {"name": "f5", "group": "Ungrouped variables", "definition": "random(10 .. 20#1)", "description": "", "templateType": "randrange"}, "x2": {"name": "x2", "group": "Ungrouped variables", "definition": "random(3 .. 4#1)", "description": "", "templateType": "randrange"}, "x3": {"name": "x3", "group": "Ungrouped variables", "definition": "random(5 .. 6#1)", "description": "", "templateType": "randrange"}, "x1": {"name": "x1", "group": "Ungrouped variables", "definition": "random(1 .. 2#1)", "description": "", "templateType": "randrange"}, "x4": {"name": "x4", "group": "Ungrouped variables", "definition": "random(7 .. 8#1)", "description": "", "templateType": "randrange"}, "x5": {"name": "x5", "group": "Ungrouped variables", "definition": "random(9 .. 10#1)", "description": "", "templateType": "randrange"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["f1", "f2", "f3", "f4", "f5", "x2", "x3", "x1", "x4", "x5"], "variable_groups": [], "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": "

$\\sum x = $  [[0]]

\n

$\\sum f = $ [[1]]

\n

$\\sum fx = $ [[2]]

\n

$\\sum fx^2 =$ [[3]]

", "stepsPenalty": 0, "steps": [{"type": "information", "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": "

$\\Sigma$ just means 'sum of' or total.

\n

For example:

\n

$\\Sigma x$ means add up the $x$ values

\n

"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{x1}+{x2}+{x3}+{x4}+{x5}", "maxValue": "{x1}+{x2}+{x3}+{x4}+{x5}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{f1}+{f2}+{f3}+{f4}+{f5}", "maxValue": "{f1}+{f2}+{f3}+{f4}+{f5}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{f1}*{x1}+{f2}*{x2}+{f3}*{x3}+{f4}*{x4}+{f5}*{x5}", "maxValue": "{f1}*{x1}+{f2}*{x2}+{f3}*{x3}+{f4}*{x4}+{f5}*{x5}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{f1}*{x1}^2+{f2}*{x2}^2+{f3}*{x3}^2+{f4}*{x4}^2+{f5}*{x5}^2", "maxValue": "{f1}*{x1}^2+{f2}*{x2}^2+{f3}*{x3}^2+{f4}*{x4}^2+{f5}*{x5}^2", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Mean", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}], "functions": {}, "ungrouped_variables": ["a1", "a3", "a2", "a5", "a4", "a7", "a6"], "tags": ["median", "mode", "Rebel", "REBEL", "rebel", "rebelmaths", "sample mean", "standard deviation", "statistics", "teame"], "preamble": {"css": "", "js": ""}, "advice": "

To find the mean: Add up all the values. Then divide by the number of values.

", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "parts": [{"prompt": "

$\\text{mean}=\\;\\;$[[0]]

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "maxValue": "1/7*{(a1+a2+a3+a4+a5+a6+a7)}", "strictPrecision": false, "minValue": "1/7*{(a1+a2+a3+a4+a5+a6+a7)}", "variableReplacementStrategy": "originalfirst", "precisionPartialCredit": 0, "correctAnswerFraction": false, "showCorrectAnswer": true, "precision": "1", "scripts": {}, "marks": "2", "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "

Calculate the mean of the following set of numbers correct to one decimal place:

\n

$\\var{a1}, \\var{a2}, \\var{a3}, \\var{a4}, \\var{a5}, \\var{a6}, \\var{a7}$ .

", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a1": {"definition": "random(9..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "a1", "description": ""}, "a3": {"definition": "random(5..6)", "templateType": "anything", "group": "Ungrouped variables", "name": "a3", "description": ""}, "a2": {"definition": "random(7..8)", "templateType": "anything", "group": "Ungrouped variables", "name": "a2", "description": ""}, "a5": {"definition": "random(0..2)", "templateType": "anything", "group": "Ungrouped variables", "name": "a5", "description": ""}, "a4": {"definition": "random(3..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "a4", "description": ""}, "a7": {"definition": "random(3..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "a7", "description": ""}, "a6": {"definition": "random(3..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "a6", "description": ""}}, "metadata": {"description": "
\n

calculating mean

\n

rebelmaths

\n
", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Averages (frequency table)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}], "functions": {}, "ungrouped_variables": ["a", "b"], "tags": ["average", "frequency table", "REBEL", "rebel", "Rebel", "rebelmaths", "teame"], "preamble": {"css": "", "js": ""}, "advice": "

See \"show steps\" within this question for more help.

", "rulesets": {}, "parts": [{"stepsPenalty": "1", "vsetrangepoints": 5, "prompt": "

What is the mean value (correct to 2 decimal places)?

", "expectedvariablenames": [], "checkingaccuracy": "2", "vsetrange": [0, 1], "showpreview": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "

To find the mean use the formula $\\frac{\\Sigma fx}{\\Sigma f}$

\n

In other words $\\frac{(0\\times\\var{f1})+(1\\times \\var{f2})+(2\\times\\var{f3})+(3\\times\\var{f4}) +(4\\times\\var{f5})+(5\\times\\var{f6})}{\\var{f1}+\\var{f2}+\\var{f3}+\\var{f4}+\\var{f5}+\\var{f6}}$

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "showCorrectAnswer": true, "scripts": {}, "answer": "{mn}", "marks": "4", "checkvariablenames": false, "checkingtype": "dp", "type": "jme"}, {"stepsPenalty": "1", "prompt": "

What is the median value?

", "allowFractions": false, "variableReplacements": [], "maxValue": "{median}", "minValue": "{median}", "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "

The median is the \"middle\" value. 

\n

In a frequency table, the observations are already arranged in an ascending order. We can obtain the median by looking for the value in the middle position.

\n

First add up the frequencies to find $n$.

\n

Case 1. When the sum of the frequencies is odd, then the median is the value at the $\\frac{n+1}{2}^{th}$ position.
Case 2. When the sum of the frequencies is even, then the median is the average of values at the positions $\\frac{n}{2}^{th}$ and $\\frac{n+1}{2}^{th}$.

\n


We need to add up the frequencies until we reach this value and then the class we land in is the median.

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": "3", "type": "numberentry", "showPrecisionHint": false}, {"stepsPenalty": "1", "prompt": "

What is the mode? (If it is undefined, enter \"0\".)

", "allowFractions": false, "variableReplacements": [], "maxValue": "1", "minValue": "1", "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "

The mode is the number which occurs most often. In other words the class with the  highest frequency.

", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": "3", "type": "numberentry", "showPrecisionHint": false}], "statement": "

Calculate the mean, the median and the mode for the following frequency table:

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Class012345
Frequency{f1}{f2}{f3}{f4}{f5}{f6}
", "variable_groups": [{"variables": ["f1", "f2", "f3", "f4", "f5", "f6"], "name": "Frequencies"}, {"variables": ["cf2", "cf3", "cf4", "cf5", "tot"], "name": "Cumulative"}, {"variables": ["a1", "a2", "a3", "a4", "a5", "mp5", "median"], "name": "Median calculations"}, {"variables": ["sfx", "mn"], "name": "Mean calculations"}], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"f1": {"definition": "random(5..20)", "templateType": "anything", "group": "Frequencies", "name": "f1", "description": ""}, "f2": {"definition": "f1+a", "templateType": "anything", "group": "Frequencies", "name": "f2", "description": ""}, "f3": {"definition": "f1-1", "templateType": "anything", "group": "Frequencies", "name": "f3", "description": ""}, "f4": {"definition": "f1-a", "templateType": "anything", "group": "Frequencies", "name": "f4", "description": ""}, "f5": {"definition": "f1-b", "templateType": "anything", "group": "Frequencies", "name": "f5", "description": ""}, "f6": {"definition": "a", "templateType": "anything", "group": "Frequencies", "name": "f6", "description": ""}, "mp5": {"definition": "tot/2", "templateType": "anything", "group": "Median calculations", "name": "mp5", "description": ""}, "tot": {"definition": "cf5+f6", "templateType": "anything", "group": "Cumulative", "name": "tot", "description": ""}, "sfx": {"definition": "0*f1+1*f2+2*f3+3*f4+4*f5+5*f6", "templateType": "anything", "group": "Mean calculations", "name": "sfx", "description": ""}, "a1": {"definition": "switch(f1mp5,0)", "templateType": "anything", "group": "Median calculations", "name": "a1", "description": ""}, "a3": {"definition": "switch(cf3mp5,0)", "templateType": "anything", "group": "Median calculations", "name": "a3", "description": ""}, "a2": {"definition": "switch(cf2mp5,0)", "templateType": "anything", "group": "Median calculations", "name": "a2", "description": ""}, "a5": {"definition": "switch(cf5mp5,0)", "templateType": "anything", "group": "Median calculations", "name": "a5", "description": ""}, "a4": {"definition": "switch(cf4mp5,0)", "templateType": "anything", "group": "Median calculations", "name": "a4", "description": ""}, "cf4": {"definition": "cf3+f4", "templateType": "anything", "group": "Cumulative", "name": "cf4", "description": ""}, "cf5": {"definition": "cf4+f5", "templateType": "anything", "group": "Cumulative", "name": "cf5", "description": ""}, "cf2": {"definition": "f1+f2", "templateType": "anything", "group": "Cumulative", "name": "cf2", "description": ""}, "cf3": {"definition": "cf2+f3", "templateType": "anything", "group": "Cumulative", "name": "cf3", "description": ""}, "a": {"definition": "random(1..f1-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "b": {"definition": "random(a..f1)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "mn": {"definition": "sfx/tot", "templateType": "anything", "group": "Mean calculations", "name": "mn", "description": ""}, "median": {"definition": "a1+a2+a3+a4+a5", "templateType": "anything", "group": "Median calculations", "name": "median", "description": ""}}, "metadata": {"description": "

rebelmaths

", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Standard deviation of a list of numbers with hints", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}], "variables": {"var": {"name": "var", "description": "", "definition": "sigma^2", "group": "Ungrouped variables", "templateType": "anything"}, "x": {"name": "x", "description": "", "definition": "random(4,5,8)", "group": "Ungrouped variables", "templateType": "anything"}, "sigma": {"name": "sigma", "description": "", "definition": "stdev(data)", "group": "Ungrouped variables", "templateType": "anything"}, "data": {"name": "data", "description": "", "definition": "repeat(random(1..30),x)", "group": "Ungrouped variables", "templateType": "anything"}, "mean": {"name": "mean", "description": "", "definition": "mean(data)", "group": "Ungrouped variables", "templateType": "anything"}}, "showQuestionGroupNames": false, "advice": "

Standard deviation = $\\sqrt{\\frac{\\Sigma (x-\\text{mean})^2}{n}}$

\n

What is the mean? Add up the numbers and divide by the number of numbers getting an answer of {mean}.

\n

Now, subtract the mean individually from each of the numbers given and square the result. 

\n

Now add up these results. This is the '$\\Sigma (x-\\text{mean})^2$' part in the formula.
Divide by {x} the number of values. This gives an answer of {var}.

\n

Finally, find the square root to get an answer of {sigma}.

", "tags": ["rebel", "Rebel", "REBEL", "rebelmaths"], "variablesTest": {"maxRuns": 100, "condition": ""}, "metadata": {"description": "

Just showing how to use the stdev function from the stats extension to calculate the standard deviation of a list of numbers.

\n

rebelmaths

", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "

Find the Standard Deviation

", "type": "question", "rulesets": {}, "functions": {}, "variable_groups": [], "ungrouped_variables": ["data", "sigma", "x", "mean", "var"], "preamble": {"js": "", "css": ""}, "parts": [{"steps": [{"type": "information", "showCorrectAnswer": true, "marks": 0, "variableReplacementStrategy": "originalfirst", "scripts": {}, "variableReplacements": [], "prompt": "

Standard deviation = $\\sqrt{\\frac{\\Sigma (x-\\text{mean})^2}{n}}$

\n

To find the standard deviation, first find the mean of the list of numbers. 

\n

What is the mean?

\n

Now, subtract the mean individually from each of the numbers given and square the result. 

\n

Now add up these results. This is the '$\\Sigma (x-\\text{mean})^2$' part in the formula.
Divide by $n$ where $n$ is the number of values.

\n

Finally, find the square root.

"}], "showCorrectAnswer": true, "precision": "1", "showPrecisionHint": false, "minValue": "{sigma}", "precisionType": "dp", "prompt": "

Find the standard deviation of the following list of numbers {data}.

\n

Give your answer correct to one decimal place.

", "precisionMessage": "

You have not given your answer to the correct number of decimal places.

", "stepsPenalty": "1", "type": "numberentry", "precisionPartialCredit": 0, "marks": "5", "correctAnswerFraction": false, "variableReplacementStrategy": "originalfirst", "scripts": {}, "strictPrecision": false, "maxValue": "{sigma}", "allowFractions": false, "variableReplacements": []}], "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "questions": [], "pickQuestions": 0}]}, {"name": "Mean, median, mode and range", "extensions": ["stats"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}], "functions": {}, "ungrouped_variables": ["a1", "a3", "a2", "a5", "a4", "a7", "a6"], "tags": ["median", "mode", "rebel", "Rebel", "REBEL", "rebelmaths", "sample mean", "standard deviation", "statistics"], "advice": "

Mean: $\\mu = \\frac{1}{N}\\sum\\limits_{i=1}^N x_i$

\n

Median: middle value

\n

Mode: most common value

\n

Range: highest value - lowest value.

", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "parts": [{"stepsPenalty": "1", "prompt": "\n

$\\text{mean}=\\;\\;$[[0]]

\n

Enter decimal answers to 3 decimal places.

\n ", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"vsetrangepoints": 5, "expectedvariablenames": [], "checkingaccuracy": 0.01, "type": "jme", "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "std", "scripts": {}, "answer": "1/7*{(a1+a2+a3+a4+a5+a6+a7)}", "marks": 3, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1]}], "steps": [{"prompt": "

To find the mean:

\n

1. Add up all the numbers.

\n

2. Divide by the number of numbers.

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$\\text{median}=\\;\\;$[[0]]

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To find the median:

\n

List the numbers in order of increasing size. 

\n

The median is then the middle number.

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$\\text{mode}=\\;\\;$[[0]]

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The mode is the number that occurs most often.

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$\\text{range}=\\;\\;$[[0]]

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Seven students were asked how they rated the online maths assessment tool numbas on a scale of 0-10, with 0 representing terrible and 10 representing excellent. The results are below. Calculate the mean, median, mode and range for the set of data.

\n

$\\var{a1}, \\var{a2}, \\var{a3}, \\var{a4}, \\var{a5}, \\var{a6}, \\var{a7}$ .

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\n

Exam covering questions on the Errorsr part of the SOEE5154M Maths course.

\n

Topics covered are calculating the mean, median, mode and standard deviation.

\n

rebelmaths

\n
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$\\frac{\\var{a}+\\var{b}+\\var{c}+\\var{d}+x}{5}=\\var{mean}$,

\n

$\\var{a}+\\var{b}+\\var{c}+\\var{d}+x=5\\times\\var{mean}$,

\n

\n

$\\var{tot}+x=\\var{g}$,

\n

$x=\\var{g}-\\var{tot}$

\n

$x=\\var{f}$

\n

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rebelmaths

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To find the mean of a set of numbers add them together and divide by the number of numbers.

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The mean of $\\var{a}, \\var{b}, \\var{c}, \\var{d}$ and $x$ is $\\var{mean}$, find the value of $x$.

\n

$x=$[[0]]

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Find the value of x given information about the mean

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