// Numbas version: exam_results_page_options {"name": "PRACTICE Maths Mini Test 1 (S2)", "metadata": {"description": "", "licence": "All rights reserved"}, "duration": 3600, "percentPass": "50", "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", "", "", "", "", "", "", "", "", ""], "variable_overrides": [[], [], [], [], [], [], [], [], [], [], [], []], "questions": [{"name": "PRAC 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/"}, {"name": "Yvonne Wancke", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3703/"}], "tags": [], "metadata": {"description": "

rebelmaths

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Use the frequency table below to calculate mean, median and and mode.

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

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

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

\n

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

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What is the median value?

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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.

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What is the mode? (If there is no mode, enter \"0\".)

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

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The student is shown two radio choices: \"Yes\" and \"No\". One of them is correct.

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A bar chart shows continuous data

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Use the table below to calculate the correlation co-efficient for the relationship between S and L

\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
S{x1}{x2}{x3}{x4}{x5}{x6}{x7}{x8}{x9}
L{y1}{y2}{y3}{y4}{y5}{y6}{y7}{y8}{y9}
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"templateType": "anything", "can_override": false}, "x7": {"name": "x7", "group": "Ungrouped variables", "definition": "random(8..11)", "description": "", "templateType": "anything", "can_override": false}, "x8": {"name": "x8", "group": "Ungrouped variables", "definition": "random(8..11)", "description": "", "templateType": "anything", "can_override": false}, "x9": {"name": "x9", "group": "Ungrouped variables", "definition": "random(8..11)", "description": "", "templateType": "anything", "can_override": false}, "y1": {"name": "y1", "group": "Ungrouped variables", "definition": "random(26..20)", "description": "", "templateType": "anything", "can_override": false}, "y2": {"name": "y2", "group": "Ungrouped variables", "definition": "random(26..20)", "description": "", "templateType": "anything", "can_override": false}, "y3": {"name": "y3", "group": "Ungrouped variables", "definition": "random(26..20)", "description": "", "templateType": "anything", "can_override": false}, "y4": {"name": "y4", "group": "Ungrouped variables", "definition": "random(22..25)", "description": "", "templateType": "anything", "can_override": false}, "y5": {"name": "y5", "group": "Ungrouped variables", "definition": "random(22..25)", "description": "", "templateType": "anything", "can_override": false}, "y6": {"name": "y6", "group": "Ungrouped variables", "definition": "random(22..25)", "description": "", "templateType": "anything", "can_override": false}, "y7": {"name": "y7", "group": "Ungrouped variables", "definition": "random(18..22)", "description": "", "templateType": "anything", "can_override": false}, "y8": {"name": "y8", "group": "Ungrouped variables", "definition": "random(18..22)", "description": "", "templateType": "anything", "can_override": false}, "y9": {"name": "y9", "group": "Ungrouped variables", "definition": "random(18..22)", "description": "", "templateType": "anything", "can_override": false}, "sumxsq": {"name": "sumxsq", "group": "Ungrouped variables", "definition": "x1^2+x2^2+x3^2+x4^2+x5^2+x6^2+x7^2+x8^2+x9^2", "description": "", "templateType": "anything", "can_override": false}, "sumysq": {"name": "sumysq", "group": "Ungrouped variables", "definition": "y1^2+y2^2+y3^2+y4^2+y5^2+y6^2+y7^2+y8^2+y9^2", "description": "", "templateType": "anything", "can_override": false}, "sumxy": {"name": "sumxy", "group": "Ungrouped variables", "definition": "x1*y1+x2*y2+x3*y3+x4*y4+x5*y5+x6*y6+x7*y7+x8*y8+x9*y9", "description": "", "templateType": "anything", "can_override": false}, "sumxallsq": {"name": "sumxallsq", "group": "Ungrouped variables", "definition": "(x1+x2+x3+x4+x5+x6+x7+x8+x9)^2", "description": "", "templateType": "anything", "can_override": false}, "sumyallsq": {"name": "sumyallsq", "group": "Ungrouped variables", "definition": "(y1+y2+y3+y4+y5+y6+y7+y8+y9)^2", "description": "", "templateType": "anything", "can_override": false}, "sumxsumy": {"name": "sumxsumy", "group": "Ungrouped variables", "definition": "(x1+x2+x3+x4+x5+x6+x7+x8+x9)*(y1+y2+y3+y4+y5+y6+y7+y8+y9)", "description": "", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "9", "description": "", "templateType": "anything", "can_override": false}, "sxx": {"name": "sxx", "group": "Ungrouped variables", "definition": "sumxsq-sumxallsq/n", "description": "", "templateType": "anything", "can_override": false}, "syy": {"name": "syy", "group": "Ungrouped variables", "definition": "sumysq-sumyallsq/n", "description": "", "templateType": "anything", "can_override": false}, "sxy": {"name": "sxy", "group": "Ungrouped variables", "definition": "sumxy-sumxsumy/n", "description": "", "templateType": "anything", "can_override": false}, "r": {"name": "r", "group": "Ungrouped variables", "definition": "sxy/(sqrt(sxx*syy))", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["x1", "x2", "x3", "x4", "x5", "x6", "x7", "x8", "x9", "y1", "y2", "y3", "y4", "y5", "y6", "y7", "y8", "y9", "sumxsq", "sumysq", "sumxy", "sumxallsq", "sumyallsq", "sumxsumy", "n", "sxx", "syy", "sxy", "r"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "6", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Calculate the correlation co-efficient

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What is shown on the y axis on a cumulative frequency graph?

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The student is shown two radio choices: \"Yes\" and \"No\". One of them is correct.

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Look at the following graph and answer the questions

\n

\n

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How many people?

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Is the data quantitative?

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How many more people do geography than maths?

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\n

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

\n

rebelmaths

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

The heights (cm) of a group of children are recorded below

\n

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

\n

Calculate the mean, median and mode of these heights.

", "advice": "

Mean: Add up all the numbers and divide by the number of numbers.

\n

Median: middle value

\n

Mode: most common value

\n

", "rulesets": {"std": ["all", "!collectNumbers", "!noLeadingMinus"]}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a7": {"name": "a7", "group": "Ungrouped variables", "definition": "random(131..140)", "description": "", "templateType": "anything", "can_override": false}, "a2": {"name": "a2", "group": "Ungrouped variables", "definition": "random(116..121)", "description": "", "templateType": "anything", "can_override": false}, "a6": {"name": "a6", "group": "Ungrouped variables", "definition": "random(126..130)", "description": "", "templateType": "anything", "can_override": false}, "a4": {"name": "a4", "group": "Ungrouped variables", "definition": "random(122..125)", "description": "", "templateType": "anything", "can_override": false}, "a1": {"name": "a1", "group": "Ungrouped variables", "definition": "random(110..115)", "description": "", "templateType": "anything", "can_override": false}, "a3": {"name": "a3", "group": "Ungrouped variables", "definition": "a2", "description": "", "templateType": "anything", "can_override": false}, "a5": {"name": "a5", "group": "Ungrouped variables", "definition": "random(126..130 except a6)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a1", "a3", "a2", "a5", "a4", "a7", "a6"], "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": "

$\\text{mean}=\\;\\;$[[0]] (correct to two decimal places)

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

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

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The table shows the marks achieved by a group of students for a maths exam.

\n\n\n\n\n\n\n\n\n\n\n\n
{a}{b}{c}{d}{f}{g}
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Calculate the mean

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The student is shown two radio choices: \"Yes\" and \"No\". One of them is correct.

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A box plot shows the median and quartiles

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Match the following terms and definitions

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Find a regression equation.

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

A school compares the exam results for students in two tests. Here are the results.

\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\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Student$\\var{obj[0]}$$\\var{obj[1]}$$\\var{obj[2]}$$\\var{obj[3]}$$\\var{obj[4]}$$\\var{obj[5]}$$\\var{obj[6]}$$\\var{obj[7]}$$\\var{obj[8]}$$\\var{obj[9]}$
First Test $(X)$$\\var{r1[0]}$$\\var{r1[1]}$$\\var{r1[2]}$$\\var{r1[3]}$$\\var{r1[4]}$$\\var{r1[5]}$$\\var{r1[6]}$$\\var{r1[7]}$$\\var{r1[8]}$$\\var{r1[9]}$
Later Score $(Y)$$\\var{r2[0]}$$\\var{r2[1]}$$\\var{r2[2]}$$\\var{r2[3]}$$\\var{r2[4]}$$\\var{r2[5]}$$\\var{r2[6]}$$\\var{r2[7]}$$\\var{r2[8]}$$\\var{r2[9]}$
", "advice": "", "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"tsqovern": {"name": "tsqovern", "group": "Ungrouped variables", "definition": "[t[0]^2/n,t[1]^2/n]", "description": "", "templateType": "anything", "can_override": false}, "a": {"name": "a", "group": "Ungrouped variables", "definition": "precround(1/n*(t[1]-spxy/ss[0]*t[0]),3)", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "precround(spxy/ss[0],3)", "description": "", "templateType": "anything", "can_override": false}, "obj": {"name": "obj", "group": "Ungrouped variables", "definition": "['A','B','C','D','E','F','G','H','I','J']", "description": "", "templateType": "anything", "can_override": false}, "r1": {"name": "r1", "group": "Ungrouped variables", "definition": "repeat(round(normalsample(67,8)),10)", "description": "", "templateType": "anything", "can_override": false}, "r2": {"name": "r2", "group": "Ungrouped variables", "definition": "map(round(a1+b1*x+random(-9..9)),x,r1)", "description": "", "templateType": "anything", "can_override": false}, "ss": {"name": "ss", "group": "Ungrouped variables", "definition": "[ssq[0]-t[0]^2/n,ssq[1]-t[1]^2/n]", "description": "", "templateType": "anything", "can_override": false}, "res": {"name": "res", "group": "Ungrouped variables", "definition": "map(precround(r2[x]-(a+b*r1[x]),2),x,0..n-1)", "description": "", "templateType": "anything", "can_override": false}, "ssq": {"name": "ssq", "group": "Ungrouped variables", "definition": "[sum(map(x^2,x,r1)),sum(map(x^2,x,r2))]", "description": "", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "10", "description": "", "templateType": "anything", "can_override": false}, "a1": {"name": "a1", "group": "Ungrouped variables", "definition": "random(10..20)", "description": "", "templateType": "anything", "can_override": false}, "ch": {"name": "ch", "group": "Ungrouped variables", "definition": "random(0..9)", "description": "", "templateType": "anything", "can_override": false}, "spxy": {"name": "spxy", "group": "Ungrouped variables", "definition": "sxy-t[0]*t[1]/n", "description": "", "templateType": "anything", "can_override": false}, "t": {"name": "t", "group": "Ungrouped variables", "definition": "[sum(r1),sum(r2)]", "description": "", "templateType": "anything", "can_override": false}, "tol": {"name": "tol", "group": "Ungrouped variables", "definition": "0.001", "description": "", "templateType": "anything", "can_override": false}, "sc": {"name": "sc", "group": "Ungrouped variables", "definition": "r1[ch]", "description": "", "templateType": "anything", "can_override": false}, "sxy": {"name": "sxy", "group": "Ungrouped variables", "definition": "sum(map(r1[x]*r2[x],x,0..n-1))", "description": "", "templateType": "anything", "can_override": false}, "b1": {"name": "b1", "group": "Ungrouped variables", "definition": "random(0.25..0.45#0.05)", "description": "", "templateType": "anything", "can_override": false}, "ls": {"name": "ls", "group": "Ungrouped variables", "definition": "precround(a+b*sc,2)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["tsqovern", "a", "b", "obj", "r1", "r2", "ss", "res", "ssq", "n", "a1", "ch", "spxy", "t", "tol", "sc", "sxy", "b1", "ls"], "variable_groups": [], "functions": {"pstdev": {"parameters": [["l", "list"]], "type": "number", "language": "jme", "definition": "sqrt(abs(l)/(abs(l)-1))*stdev(l)"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Calculate the equation of the best fitting regression line:

\n

y = a + bx

\n

Find $a$ and $b$ to 5 decimal places, then input them below to 3 decimal places. 

\n

$b=\\;$[[0]],      $a=\\;$[[1]] (enter both to 3 decimal places).

\n

", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "b-tol", "maxValue": "b+tol", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "3", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "a-tol", "maxValue": "a+tol", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Standard deviation list of numbers EXAM", "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": "Yvonne Wancke", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3703/"}], "tags": [], "metadata": {"description": "

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

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

The data below shows the number of marks for a class of students in an Accounting exam.

\n

{data}

", "advice": "

You should use the function on your calculator to find the standard deviation

", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"sigma": {"name": "sigma", "group": "Ungrouped variables", "definition": "stdev(data)", "description": "", "templateType": "anything", "can_override": false}, "data": {"name": "data", "group": "Ungrouped variables", "definition": "repeat(random(32..100),20)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["data", "sigma"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "4", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

Calculate the standard deviation

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The table shows the number of students in each year group in a school

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Year 7Year 8Year 9Year 10Year 11Year 12
{biol}{chem}{phys}{biochem}{maths}{stats}
\n

The university wants to select a sample of {sample} students to take part in a survey. 

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Complete the table below to show the percentage of students for each year.

\n

Give your answer to 1 decimal place.

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Year 7Year 8Year 9Year 10Year 11Year 12
[[0]][[1]][[2]][[3]][[4]][[5]]
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Complete the table to show the number of students needed for each year group in the sample. Remember to round your answers to the nearest whole number.

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Year 7Year 8Year 9Year 10Year 11Year 12
[[0]][[1]][[2]][[3]][[4]][[5]]
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