# 5 Data Visualization 5.6 Scatter plot

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In science, the scatterplot is widely used to present measurements of two or more related variables. It is particularly useful when the values of the variables of the y-axis are thought to be dependent upon the values of the variable of the x-axis.

In a scatterplot, the data points are plotted but not joined. The resulting pattern indicates the type and strength of the relationship between two or more variables. Chart 5.6.1 is an example of a scatterplot. Car ownership increases as the household income increases, showing that there is a positive relationship between these two variables.

Data table for Chart 5.6.1 ﻿
Data table for Chart 5.6.1
Table summary
This table displays the results of Data table for Chart 5.6.1. The information is grouped by Income (\$) (appearing as row headers), Percentage (%) (appearing as column headers).
Income (\$) Percentage (%)
20,000 60
30,000 55
40,000 75
50,000 85
60,000 82
70,000 97
80,000 87
90,000 90
100,000 95

The pattern of the data points on the scatterplot reveals the relationship between the variables. Scatterplots can illustrate various patterns and relationships, such as:

• a linear or non-linear relationship,
• a positive (direct) or negative (inverse) relationship,
• the concentration or spread of data points,
• the presence of outliers.

## Linear or non-linear relationship

When the data points form a straight line on the graph, the relationship between the variables is linear, as shown in Chart 5.6.2, Part A. When the data points don’t form a line or when they form a line that is not straight, like in Chart 5.6.2, Part B, the relationships between variables is not linear.

Data table for Chart 5.6.2 ﻿
Data table for Chart 5.6.2
Table summary
This table displays the results of Data table for Chart 5.6.2. The information is grouped by Variable X (appearing as row headers), Variable Y1 (Part A) and Variable Y2 (Part B) (appearing as column headers).
Variable X Variable Y1 (Part A) Variable Y2 (Part B)
0 -3 -2
7 4 -2
13 19 7
20 21 3
27 34 10
33 24 -5
40 42 9
47 45 9
53 58 22
60 58 25
67 71 47
73 78 71
80 77 100
87 85 160
93 90 249
100 99 392

## Positive or negative relationship

If the points cluster around a line that runs from the lower left to upper right of the graph area, then the relationship between the two variables is said to be positive or direct (Chart 5.6.3, Part A). If the points cluster around a line that runs from the upper left to the lower right of the graph area, then the relationship is said to be negative or inverse (Chart 5.6.3, Part B).

Data table for Chart 5.6.3 ﻿
Data table for Chart 5.6.3
Table summary
This table displays the results of Data table for Chart 5.6.3. The information is grouped by Variable X (appearing as row headers), Variable Y1 (Part A) and Variable Y2 (Part B) (appearing as column headers).
Variable X Variable Y1 (Part A) Variable Y2 (Part B)
0 -17 83
7 16 103
13 20 93
20 14 74
27 35 81
33 28 62
40 46 66
47 65 72
53 56 49
60 51 31
67 62 29
73 88 42
80 105 45
87 115 42
93 108 21
100 114 14

## Concentration or spread of data points

Data points can be close together (Chart 5.6.4, Part A) or spread widely across the graph area (Chart 5.6.4, Part B).

Data table for Chart 5.6.4 ﻿
Data table for Chart 5.6.4
Table summary
This table displays the results of Data table for Chart 5.6.4. The information is grouped by Variable X1 (Part A) (appearing as row headers), Variable Y1 (Part A), Variable X2 (Part B) and Variable Y2 (Part B) (appearing as column headers).
Variable X1 (Part A) Variable Y1 (Part A) Variable X2 (Part B) Variable Y2 (Part B)
44 51 4 37
42 51 25 32
48 51 64 60
49 46 15 18
38 46 51 18
41 52 60 54
55 51 20 70
50 58 35 24
54 41 15 55
59 48 47 62
42 49 62 13
55 49 35 6
52 46 60 81
46 57 65 16
55 52 70 65

## Presence of outliers

Besides portraying relationships between the variables, a scatterplot can also show whether or not there are any outliers in the data. Outliers are data points that are far from the other points in the data set, like the two points in red in Chart 5.6.5.

Data table for Chart 5.6.5 ﻿
Data table for Chart 5.6.5
Table summary
This table displays the results of Data table for Chart 5.6.5. The information is grouped by Variable X (appearing as row headers), Variable Y and Symbol (appearing as column headers).
Variable X Variable Y Symbol
0 -1 Black circle
7 1 Black circle
13 32 Black circle
15 83 Red triangle (potential outlier)
20 28 Black circle
27 5 Black circle
28 95 Red triangle (potential outlier)
33 30 Black circle
40 46 Black circle
47 29 Black circle
53 41 Black circle
60 46 Black circle
67 29 Black circle
73 54 Black circle
80 52 Black circle
87 63 Black circle
93 59 Black circle
100 82 Black circle
﻿

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