Maths Quest A Year 11 for Queensland
WorkSHEET 11.1
Chapter 11 Scatterplots and time series
WorkSHEET 11.1
1
Scatterplots and time series
Name: ___________________________
1
For each of the following determine which of
the two variables would be the dependent
variable.
(a) tree height and age
(b) flying time and aircraft speed (for given
distance)
(c) latitude and temperature
(d) thickness of a book and its mass
(e) size of a new car and its cost
(a)
(b)
(c)
(d)
(e)
tree height
flying time
temperature
mass
cost
(a)
(b)
(c)
(d)
(e)
increase
decrease
decrease
increase
increase
2
For each of the pairs of variables in question 1,
indicate whether the second variable would
increase or decrease in response to an increase
in the value of the first variable.
3
For the graphs below, indicate whether the two
variables graphed display a positive, negative
(a) no relationship
or no relationship between their values.
(b) negative
(c) positive
Maths Quest A Year 11 for Queensland
4
Chapter 11 Scatterplots and time series
The table below shows average monthly
temperature and average occupancy rate of
motel rooms in a rural locality.
Average
temperature (°C)
Number of room
nights occupied
25
20
30
18
12
6
7
8
18
20
23
26
45
40
50
47
40
28
20
16
25
30
48
50
(a) Which is the independent variable?
(b) Draw a scatterplot of the data. Interpret
the relationship between the two
variables.
(a)
WorkSHEET 11.1
Average monthly temperature is the
independent variable (put on the x-axis).
(b)
This shows moderate positive relationship
between average monthly temperature and the
number of room nights occupied.
2
Maths Quest A Year 11 for Queensland
5
Chapter 11 Scatterplots and time series
The 10 a.m. temperature (°C) and rainfall (mm)
over two weeks during the month of April in
(a)
Melbourne is shown below.
Temperature (°C)
Rainfall (mm)
5
3
16
5
20
8
10
9
14
6
8
7
18
8
13
7
9
6
17
7
7
4
14
10
4
2
3
1
(a) Which is the independent variable (put on
the x-axis)?
(b) Construct a scatterplot of rainfall against
temperature.
(b)
WorkSHEET 11.1
Temperature is the independent variable
(put on the x-axis).
3
Maths Quest A Year 11 for Queensland
6
Chapter 11 Scatterplots and time series
This table shows the hearing test scores of
people of different ages:
Age
55.0
Hearing test score
2.5
40.0
3.8
35.0
4.0
30.0
3.9
42.0
2.5
48.0
3.2
50.0
2.2
48.0
1.8
32.0
3.0
45.0
2.0
30.0
4.0
56.0
1.8
(a) Which is the independent variable (put on
the x-axis)?
(b) Construct a scatterplot showing hearing
test score against age.
(a)
(b)
WorkSHEET 11.1
The independent variable is the age (put
on the x-axis).
4
Maths Quest A Year 11 for Queensland
7
Chapter 11 Scatterplots and time series
The heights and ulna (elbow to the centre of
wrist bone) lengths of 15 Year-10 students
from Clever High are shown below.
(a)
WorkSHEET 11.1
Ulna lengths is independent (put on the
x-axis).
(b)
Ulna (cm)
Heights (cm)
26
170
28
174
25
178
25
167
24
166
23
164
25
176
26
177
25
170
27
172
25
183
26
175
(a) Which measurement is independent (put
on the x-axis)?
(b) Construct a scatterplot of height against
ulna lengths.
(c) State the type of relationship between the
two variables and draw a suitable
conclusion.
(c)
The scatterplot shows weak positive
relationship. There is evidence to suggest
that as ulna length increases, the height
also increases.
5
Maths Quest A Year 11 for Queensland
8
The table shows the number of Icy-poles sold
and the maximum temperature of the day
recorded by a shopkeeper.
Maximum
temperature
14
10
22
26
30
20
18
12
8
6
(a)
(b)
9
Chapter 11 Scatterplots and time series
Number of Icy-poles
sold
250
200
365
500
630
420
320
280
220
150
(a)
(b)
Plot the data upon a scatterplot.
State the type of relationship shown by
the scatterplot and draw a suitable
conclusion from it.
The table below shows mass and height for
men and women from 18 years upwards.
Height
(cm)
Mass (kg)
150
50
160
57
170
65
180
72
190
81
200
90
(a)
Construct a scatterplot showing this data.
(b)
State the type of relationship shown by
the scatterplot and draw a suitable
conclusion.
WorkSHEET 11.1
3
The scatterplot shows moderate positive
relationship. There is evidence to show
that the higher the temperature, the higher
the Icy-poles sales.
(a)
(b)
6
3
The scatterplot shows almost perfect
positive relationship. Clearly, higher the
height, higher the mass.
Maths Quest A Year 11 for Queensland
10
Chapter 11 Scatterplots and time series
A potato farmer records the yield in kilograms
and the length in metres of 10 commercial
potato plots as shown.
WorkSHEET 11.1
(a)
3
Length (m) Yield (kg)
10
220
6
250
16
400
2
25
13
500
7
430
4
120
12
350
5
310
8
280
(a)
Construct a scatterplot to illustrate this
data.
(b)
State the type of relationship shown by
the scatterplot and draw a suitable
conclusion.
(b)
7
The scatterplot shows positive
relationship. There is evidence to show
that as the length of the plot increases, the
yield also increases.