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Use the table below to calculate the correlation co-efficient for the relationship between science and maths grades for a group of students

\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
 Science {x1} {x2} {x3} {x4} {x5} {x6} {x7} {x8} {x9} Maths {y1} {y2} {y3} {y4} {y5} {y6} {y7} {y8} {y9}
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"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": 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"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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Rochelle has a box with {rednum} red dice and {bluenum } blue dice. She takes out one dice and does not replace it. She then takes out another dice.

\n

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What is the probability that she takes out a blue dice on the first try?

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What is the probability that she takes out a red dice on the first try?

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What is the probability that she takes out two blue dice?

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What is the probability that she takes out a blue followed by a red dice?

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What is the probability of getting one red and one blue dice?

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Match the following terms and definitions

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\n

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

\n

rebelmaths

\n
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Calculate the mean, median and mode of the numbers in this list:

\n

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

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

\n

Median: middle value

\n

Mode: most common value

\n

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$\\text{mean}=\\;\\;$[[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 number of students in each year group of a school are shown in the table below.

\n

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
 Year 5 6 7 8 9 Number of students {Y5} {Y6} {Y7} {Y8} {Y9}
\n

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How many students are there in the school?

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A student is selected at random. What is the probability that they are in year 9? Give your answer as a fraction.

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Another student is selected at random from all of the students in the school. What is the probability that they are in years 5, 6 or 7? Give your answer as a fraction.

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The table shows the number of students studying particular subjects in a college. (Students only study one of these courses)

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
 Biology Chemistry Physics Biochemistry Maths Statistics {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 course.

\n

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
 Biology Chemistry Physics Biochemistry Maths Statistics [[0]] [[1]] [[2]] [[3]] [[4]] [[5]]

Complete the table to show the number of students needed for each course 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
 Biology Chemistry Physics Biochemistry Maths Statistics [[0]] [[1]] [[2]] [[3]] [[4]] [[5]]

Marlene is learning to drive. The probability that she passes her driving test on any attempt is {pass}

\n

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What is the probability that she passes at the first attemot?

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\n
1. What is the probability that she passes at the third attempt?
2. \n
\n

Hint: once she passes she won't take the test again!

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What is the probability that she passes in fewer than 4 attempts?

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This question gives some information about which newspaper is read by a group of people.

\n

", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"diagram": {"name": "diagram", "group": "Ungrouped variables", "definition": "eukleides(\"A Venn diagram with {justA} in just The Times, {justB} in just The Guardian, {both} in both, and {neither} in neither\",\n[\ncircle(point(0,0),2) color1 filled opacity(0.5),\npoint(-1,2) label(\"The Guardian\",deg(180)),\ncircle(point(3,0),2) color2 filled opacity(0.5),\npoint(4,2) label(\"The Independent\",deg(0)),\npoint(0,0) label(justA,deg(180)),\npoint(3,0) label(justB,deg(0)),\npoint(1.5,0) label(both,0),\npoint(6,0) label(neither)\n],\n[\"justA\":justA,\"justB\":justB,\"both\":both,\"neither\":neither]\n)", "description": "", "templateType": "anything", "can_override": false}, "groups": {"name": "groups", "group": "Ungrouped variables", "definition": "[\n [25,30,10,35],\n [20,40,25,15],\n [15,50,20,15],\n [20,35,15,30],\n [10,30,15,45]\n]", "description": "", "templateType": "anything", "can_override": false}, "group": {"name": "group", "group": "Ungrouped variables", "definition": "random(groups)", "description": "", "templateType": "anything", "can_override": false}, "justA": {"name": "justA", "group": "Ungrouped variables", "definition": "group[0]", "description": "", "templateType": "anything", "can_override": false}, "justB": {"name": "justB", "group": "Ungrouped variables", "definition": "group[1]", "description": "", "templateType": "anything", "can_override": false}, "both": {"name": "both", "group": "Ungrouped variables", "definition": "group[2]", "description": "", "templateType": "anything", "can_override": false}, "neither": {"name": "neither", "group": "Ungrouped variables", "definition": "group[3]", "description": "", "templateType": "anything", "can_override": false}, "p": {"name": "p", "group": "Ungrouped variables", "definition": "(justA+justB)/(justA+justB+both+neither)", "description": "", "templateType": "anything", "can_override": false}, "pb": {"name": "pb", "group": "Ungrouped variables", "definition": "both/(justA+justB+both+neither)", "description": "", "templateType": "anything", "can_override": false}, "ponlyGuardian": {"name": "ponlyGuardian", "group": "Ungrouped variables", "definition": "justB/(justA+justB+both+neither)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["groups", "group", "justA", "justB", "both", "neither", "diagram", "p", "pb", "ponlyGuardian"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": false, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "

The diagram shows the percentage of people who read The Guardian and/or The Independent.

\n

{max_width(30,diagram)}

\n

What is the probability that a person chosen randomly reads only one of these newspapers?

\n

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What is the probability that a randomly chosen person reads both?

\n

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What is the probability that a randomly chosen person reads only The Independent?

\n

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Find a regression equation.

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

A college 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 regression line: \n y = a + b$$x$

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

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

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