and the extreme values of the interval are only achieved in case the data pairs are perfectly
correlated, implying that the points on the scatter diagram lie on a straight line. For the
example shown in Figure 2.2 there is almost zero correlation at the left hand side and almost
full positive correlation at the right hand side.
2.6 Graphical Representations
Graphical representations provide a convenient and strong basis for assessing data and to
communicate these to other persons. There exist a relatively large number of different
possible graphical representations of data, of which some are better suited than others
depending on the purpose of the representations. Some are better for representing the
characteristics of data sets containing observations of one characteristic, like e.g. the concrete
compressive strength and others are better for representing the characteristics of two or more
data sets (e.g. the simultaneously observed traffic flows). In the following, the most frequently
applied graphical representations are introduced and discussed with the help of examples.
One-Dimensional Scatter Diagrams
The simplest graphical representation is the scatter diagram which provides a means to
represent observations contained in one or more data sets. The scatter diagram may be
constructed by plotting the observed values of the data set along an axis labelled according to
the scale of the observations. In a one-dimensional scatter diagram the minimum and
maximum values of the data set can be readily observed. Furthermore, as long as the number
of data is not very large, the central value of the observed data may be observed directly from
the plot. In the case where a data set contains a large number of data, some of these may be
overlapping and this makes it difficult to distinguish the individual observations. In such cases
it may be beneficial to apply another graphical representation such as histograms, as described
subsequently.
Consider the data set corresponding to the concrete cube compressive strength measurements
from Table 2.2. The corresponding one-dimensional scatter diagram is given in Figure 2.3. It
can be seen that the data are relatively widely distributed and there are not many overlaps.
Figure 2.3: One-dimensional scatter plot of the concrete cube compressive strength data.
Histograms
A frequently applied graphical representation of data sets is the histogram. Consider again as
an example the concrete cube compressive strength data from Table 2.2. The data are further
processed and the observed compressive strengths are subdivided into intervals, see Table 2.4.
For each interval the mid point is determined and the number of observations within each