Exercises for Question Type 5: Describing the correlation

Question 1

Skill question

A scatter diagram shows points lying close to a straight line sloping downward from left to right. Describe the type and strength of the correlation.

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Question 2

Skill question

The following data pairs $(x, y)$ describe a relationship between two variables: $(1, 2), (2, 4), (3, 6), (4, 8), and (10, 0)$ The point $(10, 0)$ is identified as an outlier.

A grid for plotting the data is provided below.

1.

Plot all five data points on the scatter diagram provided.

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2.

Draw a line of best fit for this data, ignoring the outlier $(10, 0)$ .

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3.

Describe how the inclusion of the outlier $(10, 0)$ affects the overall correlation of the data set.

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4.

Using your line of best fit, estimate the value of $y$ when $x = 5$ .

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Question 3

Skill question

The following table shows the values of $x$ and $y$ for a set of bivariate data.

$x$	1	2	3	4	5	6
$y$	10	9	7	6	5	3

1.

Plot a scatter diagram for this data.

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2.

Draw a line of best fit on your scatter diagram.

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3.

Describe the correlation between $x$ and $y$ .

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4.

Using your line of best fit, estimate the value of $y$ when $x = 4.5$ .

[1]

Question 4

Skill question

The following data relates the variables $x$ and $y$ :

$(1, 3), (2, 5), (3, 6), (4, 8), (5, 9)$

1.

Plot a scatter diagram for this data.

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2.

Draw the line of best fit on your scatter diagram.

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3.

Use your line of best fit to estimate the value of $y$ when $x = 6$ .

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Question 5

Skill question

A student records the number of hours studied ( $x$ ) and the corresponding exam scores ( $y$ ) for five different students, as shown in the table below:

Hours Studied ( $x$ )	2	4	6	8	10
Exam Score ( $y$ )	50	65	75	85	90

1.

Plot a scatter diagram for this data, using a scale of 1 cm to represent 1 hour on the $x$ -axis and 1 cm to represent 10 units on the $y$ -axis.

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2.

Sketch the line of best fit on your scatter diagram.

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3.

Describe the correlation between the hours studied and the exam score.

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4.

Use your line of best fit to predict the exam score for a student who studied for 7 hours.

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Question 6

Skill question

Given the data pairs $(1, 2)$ , $(2, 3)$ , $(3, 5)$ , $(4, 6)$ , and $(5, 7)$ , plot the scatter diagram, draw a line of best fit by eye, and describe the correlation.

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IB Mathematics Applications & Interpretation Question Type 5: Describing the Correlation Exercises

IB Mathematics Applications & Interpretation Question Type 5: Describing the Correlation Exercises