Graphics Reference
In-Depth Information
BASIC WAYS OF GRAPHICAL
DISPLAY OF THE DATA
Usually, the variables depend on each other. For
example, if we have two variables, they are related
in such a way that when we change the value of
the first variable, we can determine the value of
the second variable. The first variable is called the
independent and the second the dependent variable.
We use axes x and y to display the relationship of
independent and dependent variables visually. We
place independent variable (for example, time) at
the horizontal axis (x) (we call point 0 the origin)
and then we show values of the dependent variable
(which changes in time, for example, distance) at
the vertical axis (y). When we want to determine
location of a point P on a two-dimensional plane
in a Cartesian coordinate system, we talk about the
x-coordinate or abscissa (it is positive if P is to the
right of the y-axis) and the y-coordinate or ordinate
(which is positive, negative, or zero if P is above,
below, or on the x-axis). On our data graphics,
the point P with coordinates (x, y) is represented
as P (x, y). We may draw a graph (a straight line
or a curve) that shows a collection of such points
as a function representing relation between the
independent and dependent variable.
When we want to describe a process, we have
to look over characteristic traits of the object.
When we want to describe how this object will
change when conditions become different, we
have to state what kinds of changes we are going
to measure, that means, we have to list variables.
For example, we may measure how a distance
will change depending on the time (duration) of
our traveling, or how the duration of our travel-
ing will depend on its speed. Thus the variables
represent characteristic traits, which take on dif-
ferent values (exact amounts or numbers) under
changing conditions. Many times, when we draw a
graphic presentation of an algebraic or geometric
relationship, a chart, a graph, or a sketch, there are
many variables dependent on each other and it is
a real challenge to visualize them in one graph.
When we want to visualize these variables, we
can think about their dimensions.
See Table 2 for Your Visual Response.
Dimensions, Variables, and
Coordinate Systems
Basic concepts employed in visualization involve
such notions as dimension and variable. According
to Edward Tufte (1983), talking is a linear, non-
reversible, one-dimensional sequence. Graphics
overcome those restrictions and allow the viewers
to reason about a multidimensional array of data
at their own pace and in their own manner, com-
municate, document, and preserve knowledge.
Basic concepts employed in visualizing higher
dimensions include a mathematical definition
of dimension as the measure of a distance of
a single point from the origin of an axis (Cox,
2008). Visualizing higher dimensions requires
specifying the position of a point. The number of
measurements needed to determine the locus of a
point depends on the number of dimensions. Thus,
a line is one-dimensional because all is needed
is one measurement of the distance between a
point and the origin of an axis. In order to draw
a two-dimensional plot on a plane, two measure-
ments are needed to specify the distance of the
point from the origin of the x and the y axes. To
position a single point in three-dimensional space,
three measurements are needed, along the x, y,
and z axes.
The data are often described by sets of num-
bers. When we examine an object or a process, we
determine some of its features. We measure the
values of the variables, for example, geometrical
dimensions of the object (how long, wide, or high is
the object), its temperature, pressure, changes over
time, etc. If our numbers do not change, the variable
becomes a constant. The concept of dimension is
related to the number of represented variables. A
variable is a measurable whole to which we may
ascribe a set of values. We use symbols of such
wholes, for example, in the expression a 2 + b 2 =
c 2 , a, b, and c are variables.
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