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Question 1

A pharmaceutical trial records drug dosage $(x)$ in mg and blood pressure reduction $(y)$ in mmHg: $(10,5)$ , $(20,12)$ , $(30,18)$ , $(40,25)$ , $(50,28)$ . Plot the scatter diagram, draw a line of best fit, and estimate the dose required for a $35 \text{ mmHg}$ reduction.

[5]

Question 2

The data below show hours studied $(x)$ and exam scores $(y)$ for six students: $(2,60)$ , $(3,65)$ , $(5,75)$ , $(6,80)$ , $(8,90)$ , $(9,95)$ . Plot a scatter diagram, draw a line of best fit by eye, and estimate the exam score for a student who studies for 7 hours.

[5]

Question 3

The points $(1,2)$ , $(2,4)$ , $(3,6)$ and $(4,8)$ are plotted on a scatter diagram below.

Scatter diagram

Describe the type and strength of the correlation and, by eye, draw the line of best fit.

[3]

Question 4

A biologist records the age ( $x$ ) in years and height ( $y$ ) in metres of saplings: $(1,1.2)$ , $(2,2.3)$ , $(3,3.1)$ , $(4,3.8)$ , $(5,4.5)$ .

Plot these points on a scatter diagram, draw a line of best fit, and estimate the height at $2.5$ years.

[4]

Question 5

A café records daily mean temperature ( $x$ ) in $^\circ\text{C}$ and cups of hot chocolate sold ( $y$ ): $(5, 120)$ , $(10, 90)$ , $(15, 60)$ , $(20, 40)$ , $(25, 20)$ , $(30, 10)$ .

Plot a scatter diagram, draw a line of best fit, and estimate the sales at $18^\circ\text{C}$ .

[5]

Question 6

A dataset of children’s weight $(x)$ in kg and height $(y)$ in cm is: $(30, 130)$ , $(35, 140)$ , $(40, 150)$ , $(45, 160)$ , $(95, 155)$ . Plot a scatter diagram, draw a line of best fit ignoring the outlier $(95, 155)$ , and estimate the height at $50 \text{ kg}$ .

[4]

Question 7

The following table shows the data for two variables $x$ and $y$ .

$x$	0	2	4	6	8
$y$	2	5	9	12	16

1.

Plot a scatter diagram for this data.

[2]

2.

Draw a line of best fit through the data points.

[1]

3.

Determine the approximate equation of the line of best fit by selecting two points on the line.

[3]

4.

Using your equation, predict the value of $y$ when $x=10$ .

[2]

Question 8

Reaction time $(y)$ in seconds is measured against hours of sleep $(x)$ for six volunteers: $(4, \, 0.6)$ , $(5, \, 0.5)$ , $(6, \, 0.4)$ , $(7, \, 0.35)$ , $(8, \, 0.3)$ , $(9, \, 0.28)$ .

Plot a scatter diagram, draw a best-fit line by eye, and estimate the reaction time at $6.5$ hours of sleep.

[5]

Question 9

Engine size $(x)$ in litres and fuel consumption $(y)$ in L/100 km are recorded for six cars: $(1.0, 6.0)$ , $(1.2, 6.5)$ , $(1.4, 7.0)$ , $(1.6, 7.5)$ , $(1.8, 8.0)$ , $(2.0, 8.5)$ . Plot a scatter diagram, draw a line of best fit, and estimate the consumption at $x=1.5 \text{ L}$ .

[5]

Question 10

Rainfall $(x)$ in mm and crop yield $(y)$ in tonnes per hectare are recorded: $(100, 2.0)$ , $(200, 3.5)$ , $(300, 4.8)$ , $(400, 6.0)$ , $(500, 6.5)$ . Plot the data, draw a line of best fit by eye, and estimate the yield when rainfall is $250 \text{ mm}$ .

[5]

Question 11

The floor area $x$ , in $\text{m}^2$ , and sale price $y$ , in thousands of dollars, for five houses are given in the following table.

\begin{array}{|c|c|c|c|c|c|} \hline x & 50 & 70 & 90 & 110 & 130 \\ \hline y & 100 & 150 & 180 & 210 & 260 \\ \hline \end{array}

Plot these points on a suitable pair of axes, draw a line of best fit, and estimate the sale price for a $100 \text{ m}^2$ house.

[5]

Question 12

1.

The class size $(x)$ and average test score $(y)$ for six classes are shown in the table below:

\begin{array}{|l|c|c|c|c|c|c|} \hline \text{Class size } (x) & 10 & 20 & 30 & 40 & 50 & 60 \\ \hline \text{Test score } (y) & 78 & 75 & 72 & 70 & 68 & 65 \\ \hline \end{array}

Plot a scatter diagram for this data. Use a scale of $0 \le x \le 70$ and $60 \le y \le 80$ .

[2]

2.

Draw a line of best fit by eye on the scatter diagram.

[1]

3.

Use your line of best fit to estimate the average score for a class of 25 students.

[2]

4.

Comment on the correlation between class size and average test score.

[1]

Question Type 4: Using bivariate data to plot scatter diagrams Exercises