Scatter Graphs
Scatter graphs are used to show whether there is a relationship
between two sets of data. The relationship between the data can be
described as either:
1. A positive correlation. As one quantity increases so does the other.
2. A negative correlation. As one quantity increases the other decreases.
Shoe Size
Height
Soup Sales
3. No correlation. Both quantities vary with no clear relationship.
Shoe Size
Temperature
Positive Correlation
Negative correlation
Annual Income
No correlation
Scatter Graphs
Scatter graphs are used to show whether there is a relationship
between two sets of data. The relationship between the data can be
described as either:
1. A positive correlation. As one quantity increases so does the other.
2. A negative correlation. As one quantity increases the other decreases.
3. No correlation. Both quantities vary with no clear relationship.
Shoe Size
Shoe Size
Height
Soup Sales
A negative
positive correlation
correlation is
is characterised
characterised by
by aa straight
straight line
line with
with aa positive
negativegradient.
gradient.
Temperature
Annual Income
Negative
3
None
Height
(mpg)
2
Petrol consumption
Positive
Negative
Outside air temperature
5
Positive
Sales of Ice Cream
4
Sales of Sun cream
KS 3 Results
Car engine size (cc)
Maths test scores
There
with
no relationship
higher
maths
between
scores
tend
KS
3to
results
get
higher
and the
physics
height
scores.
of
students.
As
People
theis
tend
engine
outside
tosize
buy
air temperature
of
less
more
cars
ice
sun
increase,
cream
cream
increases,
inwhen
rainier
they
the
use
heating
weather.
weather
more
bills
petrol.
is
will
sunnier.
(Less
be
lower.
mpg)
Heating bill (£)
1
Physics test scores
State the type of correlation for the scatter graphs below
and write a sentence describing the relationship in each case.
6
Negative
Daily hours of sunshine Daily rainfall totals (mm)
A positive or negative correlation is characterised by a straight line
with a positive /negative gradient. The strength of the correlation
depends on the spread of points around the imagined line.
Strong Positive
Strong negative
Moderate Positive
Weak Positive
Moderate Negative
Weak negative
Drawing a Line of Best Fit
A line of best fit can be drawn to data that shows a correlation. The
stronger the correlation between the data, the easier it is to draw
the line. The line can be drawn by eye and should have roughly the
same number of data points on either side.
Lobf
The sum of the vertical distances above the line should be roughly
the same as those below.
(1). The
table below
shoe size and mass of
10 men.
Plotting
theshows
datathe
points/Drawing
a line
of
(a) Plot a scatter
for this data andquestions.
draw a line of best fit.
bestgraph
fit/Answering
Size
5
12
7
10
10
9
8
11
6
8
Mass
65
97
68
92
78
78
76
88
74
80
Mass (kg)
100
95
90
85
80
75
70
65
60
4
5
6 7 8 9 10 11 12 13
Shoe Size
Question 1
(1). The table below shows the shoe size and mass of 10 men.
(a) Plot a scatter graph for this data and draw a line of best fit.
Size
5
12
7
10
10
9
8
11
6
8
Mass
65
97
68
92
78
78
76
88
74
80
Mass (kg)
100
95
90
85
80
75
70
65
60
4
5
6 7 8 9 10 11 12 13
Shoe Size
(1). The table below shows the shoe size and mass of 10 men.
(a) Plot a scatter graph for this data and draw a line of best fit.
Size
5
12
7
10
10
9
8
11
6
8
Mass
65
97
68
92
78
78
76
88
74
80
Mass (kg)
100
95
90
85
80
75
70
65
60
4
5
6 7 8 9 10 11 12 13
Shoe Size
(1). The table below shows the shoe size and mass of 10 men.
(a) Plot a scatter graph for this data and draw a line of best fit.
Size
5
12
7
10
10
9
8
11
6
8
Mass
65
97
68
92
78
78
76
88
74
80
Mass (kg)
100
95
90
85
80
75
70
65
60
4
5
6 7 8 9 10 11 12 13
Shoe Size
(1). The table below shows the shoe size and mass of 10 men.
(a) Plot a scatter graph for this data and draw a line of best fit.
Size
5
12
7
10
10
9
8
11
6
8
Mass
65
97
68
92
78
78
76
88
74
80
Mass (kg)
100
95
90
85
80
75
70
65
60
4
5
6 7 8 9 10 11 12 13
Shoe Size
(1). The table below shows the shoe size and mass of 10 men.
(a) Plot a scatter graph for this data and draw a line of best fit.
Size
5
12
7
10
10
9
8
11
6
8
Mass
65
97
68
92
78
78
76
88
74
80
Mass (kg)
100
95
90
85
80
75
70
65
60
4
5
6 7 8 9 10 11 12 13
Shoe Size
(1). The table below shows the shoe size and mass of 10 men.
(a) Plot a scatter graph for this data and draw a line of best fit.
Size
5
12
7
10
10
9
8
11
6
8
Mass
65
97
68
92
78
78
76
88
74
80
Mass (kg)
100
95
90
85
80
(b) Draw a line of best fit
and comment on the
correlation. Positive
87 kg
(c) Use your line of best fit
to estimate:
75
70
65
(i)
Size 6
60
4
5
6 7 8 9 10 11 12 13
Shoe Size
The mass of a man with
shoe size 10½.
(ii) The shoe size of a man
with a mass of 69 kg.
(2).The table below shows the number of people who visited a museum
over a 10 day period last summer together with the daily sunshine totals.
(a) Plot a scatter graph for this data and draw a line of best fit.
6
0.5
8
3
8
10
Visitors
300
475
100
390
200
50
Number of Visitors
Hours Sunshine
7
5
3
2
175 220 350 320
500
450
400
350
300
250
200
150
100
0 1
2
3 4 5 6 7 8 9 10
Hours of Sunshine
Question2
(2).The table below shows the number of people who visited a museum
over a 10 day period last summer together with the daily sunshine totals.
(a) Plot a scatter graph for this data and draw a line of best fit.
6
0.5
8
3
8
10
Visitors
300
475
100
390
200
50
Number of Visitors
Hours Sunshine
500
450
400
350
300
250
200
150
100
0 1
2
3 4 5 6 7 8 9 10
Hours of Sunshine
7
5
3
2
175 220 350 320
(2).The table below shows the number of people who visited a museum
over a 10 day period last summer together with the daily sunshine totals.
(a) Plot a scatter graph for this data and draw a line of best fit.
6
0.5
8
3
8
10
Visitors
300
475
100
390
200
50
Number of Visitors
Hours Sunshine
500
450
400
350
300
250
200
150
100
0 1
2
3 4 5 6 7 8 9 10
Hours of Sunshine
7
5
3
2
175 220 350 320
(2).The table below shows the number of people who visited a museum
over a 10 day period last summer together with the daily sunshine totals.
(a) Plot a scatter graph for this data and draw a line of best fit.
6
0.5
8
3
8
10
Visitors
300
475
100
390
200
50
Number of Visitors
Hours Sunshine
500
450
400
350
300
250
200
150
100
0 1
2
3 4 5 6 7 8 9 10
Hours of Sunshine
7
5
3
2
175 220 350 320
(2).The table below shows the number of people who visited a museum
over a 10 day period last summer together with the daily sunshine totals.
(a) Plot a scatter graph for this data and draw a line of best fit.
6
0.5
8
3
8
10
Visitors
300
475
100
390
200
50
Number of Visitors
Hours Sunshine
500
450
5
3
2
175 220 350 320
(b) Draw a line of best fit
and comment on the
correlation. Negative
400
350
300
250
7
(c) Use your line of best fit
to estimate:
310
(i)
200
150
5½
100
0 1
2
3 4 5 6 7 8 9 10
Hours of Sunshine
The number of visitors
for 4 hours of sunshine.
(ii) The hours of sunshine
when 250 people visit.
(1). The table below shows the shoe size and mass of 10 men.
(a) Plot a scatter graph for this data and draw a line of best fit.
Size
5
12
7
10
10
9
8
11
6
8
Mass
65
97
68
92
78
78
76
88
74
80
(b) Draw a line of best fit
and comment on the
correlation.
Mass (kg)
100
95
90
85
80
If you have a calculator you
can find the mean of each
set of data and plot this
point to help you draw the
line of best fit. Ideally all
lines of best fit should pass
through:
(mean data 1, mean data 2)
In this case: (8.6, 79.6)
75
70
65
60
4
5
6 7 8 9 10 11 12 13
Shoe Size
Means 1
(2).The table below shows the number of people who visited a museum
over a 10 day period last summer together with the daily sunshine totals.
(a) Plot a scatter graph for this data and draw a line of best fit.
6
0.5
8
3
8
10
Visitors
300
475
100
390
200
50
Number of Visitors
Hours Sunshine
500
450
5
3
2
175 220 350 320
(b) Draw a line of best fit
and comment on the
correlation.
400
If you have a calculator you
can find the mean of each
set of data and plot this
point to help you draw the
line of best fit. Ideally all
lines of best fit should pass
through co-ordinates:
(mean data 1, mean data 2)
In this case: (5.2, 258))
350
300
250
200
150
100
0 1
7
2
3 4 5 6 7 8 9 10
Hours of Sunshine
Means
Mean 2
(1.) The table below shows the shoe size and mass of 10 men.
(a) Plot a scatter graph for this data and draw a line of best fit.
Size
5
12
7
10
10
9
8
11
6
8
Mass
65
97
68
92
78
78
76
88
74
80
Mass (kg)
100
95
90
85
80
75
70
65
60
4
5
6 7 8 9 10 11 12 13
Shoe Size
Worksheet 1
(2).The table below shows the number of people who visited a museum
over a 10 day period last summer together with the daily sunshine totals.
(a) Plot a scatter graph for this data and draw a line of best fit.
6
0.5
8
3
8
10
Visitors
300
475
100
390
200
50
Number of Visitors
Hours Sunshine
7
5
3
2
175 220 350 320
500
450
400
350
300
250
200
150
100
0 1
2
3 4 5 6 7 8 9 10
Hours of Sunshine
Worksheet 2