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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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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

Give your answers as fractions

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

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 $\\var{a4}$.

", "advice": "

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
Year56789
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
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 course.

\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
BiologyChemistryPhysicsBiochemistry MathsStatistics
[[0]][[1]][[2]][[3]][[4]][[5]]
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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
BiologyChemistryPhysicsBiochemistry MathsStatistics
[[0]][[1]][[2]][[3]][[4]][[5]]
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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"}, {"name": "S2 EXAM Tree 3", "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": "None specified"}, "statement": "

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

\n

Answer the following questions.

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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

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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

Give your answer as a fraction.

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

\n

Give your answer as a fraction.

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

\n

Give your answer as a fraction.

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Find a regression equation.

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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]}$
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Calculate the equation of the regression line:

\n

y = $a$ + $b$$x$

\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

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