// Numbas version: finer_feedback_settings {"name": "Maths Mini Test 1 (S2)", "metadata": {"description": "", "licence": "All rights reserved"}, "duration": 5400, "percentPass": "50", "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", "", "", "", "", "", "", ""], "variable_overrides": [[], [], [], [], [], [], [], [], [], []], "questions": [{"name": "Q1 MT1 S2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Yvonne Wancke", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3703/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "

The table shows the weekly profit from a small local shop.

\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 bar chart can show qualitative data

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Match the following terms and definitions

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rebelmaths

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

Calculate the mean, the median and the mode of the data from the following frequency table below:

\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}
", "advice": "

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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What is the median value?

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

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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": "

Here are the marks for 20 students in a test

\n

{data}

", "advice": "

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

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Calculate the standard deviation

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A science faculty in a university has a total of {pop} students. The table below shows the subjects studied by the students. No student studies moew than one subject.

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
BiologyChemistryPhysicsBiochemistryMathsStatistics
{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 subject.

\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
Biology   ChemPhysicsBiochemMathsStatistics
[[0]][[1]][[2]][[3]][[4]][[5]]
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"extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "P2", "maxValue": "P2", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "1", "precisionPartialCredit": "75", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "P3", "maxValue": "P3", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "1", "precisionPartialCredit": "75", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "P4", "maxValue": "P4", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "1", "precisionPartialCredit": "75", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "P5", "maxValue": "P5", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "1", "precisionPartialCredit": "75", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "P6", "maxValue": "P6", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "1", "precisionPartialCredit": "75", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"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": "

Complete thet table to show the number of students needed for each subject 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
BiologyChemPhysicsBiochemMathsStatistics
[[0]][[1]][[2]][[3]][[4]][[5]]
", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [{"variable": "P1", "part": "p0g0", "must_go_first": false}], "variableReplacementStrategy": "alwaysreplace", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "N1", "maxValue": "N1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": 0, "precisionPartialCredit": "75", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [{"variable": "P2", "part": "p0g1", "must_go_first": false}], "variableReplacementStrategy": "alwaysreplace", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "N2", "maxValue": "N2", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": 0, "precisionPartialCredit": "75", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [{"variable": "P3", "part": "p0g2", "must_go_first": false}], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "N3", "maxValue": "N3", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": 0, "precisionPartialCredit": "75", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [{"variable": "P4", "part": "p0g3", "must_go_first": false}], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "N4", "maxValue": "N4", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": 0, "precisionPartialCredit": "75", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [{"variable": "P5", "part": "p0g4", "must_go_first": false}], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "N5", "maxValue": "N5", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": 0, "precisionPartialCredit": "75", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [{"variable": "P6", "part": "p0g5", "must_go_first": false}], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "N6", "maxValue": "N6", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": 0, "precisionPartialCredit": "75", "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "Correlation co-efficient (PMCC)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Yvonne Wancke", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3703/"}], "tags": [], "metadata": {"description": "", "licence": "All rights reserved"}, "statement": "

Here is some data about two variables, x and y

\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
x{x1}{x2}{x3}{x4}{x5}{x6}{x7}{x8}{x9}
y{y1}{y2}{y3}{y4}{y5}{y6}{y7}{y8}{y9}
", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"x1": {"name": "x1", "group": "Ungrouped variables", "definition": "random(6..8)", "description": "", "templateType": "anything", "can_override": false}, "x2": {"name": "x2", "group": "Ungrouped variables", "definition": "random(6..8)", "description": "", "templateType": "anything", "can_override": false}, "x3": {"name": "x3", "group": "Ungrouped variables", "definition": "random(6..8)", "description": "", "templateType": "anything", "can_override": false}, "x4": {"name": "x4", "group": "Ungrouped variables", "definition": "random(7..9)", "description": "", "templateType": "anything", "can_override": false}, "x5": {"name": "x5", "group": "Ungrouped variables", "definition": "random(7..9)", "description": "", "templateType": "anything", "can_override": false}, "x6": {"name": "x6", "group": "Ungrouped variables", "definition": "random(7..9)", "description": "", "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(20..22)", "description": "", "templateType": "anything", "can_override": false}, "y2": {"name": "y2", "group": "Ungrouped variables", "definition": "random(20..22)", "description": "", "templateType": "anything", "can_override": false}, "y3": {"name": "y3", "group": "Ungrouped variables", "definition": "random(20..22)", "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(24..26)", "description": "", "templateType": "anything", "can_override": false}, "y8": {"name": "y8", "group": "Ungrouped variables", "definition": "random(24..26)", "description": "", "templateType": "anything", "can_override": false}, "y9": {"name": "y9", "group": "Ungrouped variables", "definition": "random(24..26)", "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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Johanna wants to plot a cumulative frequency graph. Answer the questions below to help her.

", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

What should she plot for the x value?

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What should she show on the y axis?

", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "dropdownlist", "displayColumns": 0, "showCellAnswerState": false, "choices": ["the cumulative frequency", "the upper value of the groups from the table", "the frequency", "the mid-points"], "matrix": ["2", 0, 0, 0], "distractors": ["", "", "", ""]}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

What is the inter-quartile range?

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Match the following values of correlation co-efficients with the descriptions

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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]}$
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Calculate the equation of the best fitting regression line:

\n

y = a + bx

\n

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

\n

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

\n

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

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