There is considerable confusion when it comes to giving accurate definitions of the terms: Diagram, Graph, and Chart. How do they differ? Where is each one of these types of graphical representation of information used?

This confusion is multiplied when one realises that dictionaries do not give accurate definitions or that they use the terms (especially graph and chart) interchangeably. Even more, there are cases where dictionaries give conflicting definitions of the terms or present examples of graphical representations that will in one case be referred to as graphs and in another as charts.

I believe that it is in order to alleviate this confusion. It is time to get educational baby!

This short paper will attempt to accurately define the terms and provide examples. This is not my work. What is mine is the selection and appropriate editing of relative online material as well as some inline comments and explanations.

Part 1: A first attempt

Charts

Definition: A chart is the visualization of the situation of an entity at some point in time or space.

The basic types of Charts are:

¨ Pie Chart: e.g. allocation of funds in a budget

¨ Area Chart: e.g. allocation of funds in a budget over the years

¨ Table Chart: e.g. figures of budgets related to various years

¨ Bar/Column Chart: e.g. income of groups of people

¨ Picto Chart : using pictorial symbols to visualize Information

¨ Geographical Chart : a map of a region (physical map, political map, economic map, etc.)

Graphs

Definition: A Graph is the visualization of the relation(s) among a number of entities.

Oxford Science Dictionary Definition: A diagram that illustrates the relationship between two variables.

The most common type of a Graph is:

¨ Line Graph (or Dots Graph): e.g. relational variations of entities (variables)

· A Line Graph uses the Cartesian Coordinates with:

§ horizontal axis: independent variable (x)

§ vertical axis: dependent variable (y)

· A line graph can involve more than two entities: e.g. for 3 variables we can have 3 axes and 3-dimensional graphs

Comment 1: According to the Chart and Graph definitions above one could say that a graph is a more general case of a chart, since a graph depicts the relation between any two (or more) entities-variables, while a chart depicts the relation between an entity-variable and a specific time-place (in effect a variable that stays constant). However, this assertion is quite wrong mainly due to shallow observation of the functional specifics of a chart. Specifically, a graph between two variables (say velocity over time) would not convey much info at all, if time was constant. We can now easily see that for a graph to convey info (and therefore be a graph) all (or both if they are only two) entities need to be variable. In fact, a graph with entities (or one of the entities if there are only two) that are not variable cannot be conceived as then the very concept of “relation” (between those entities) is undefined. We will see, later on, that the info conveyed by charts is not relational between variables-entities but mainly of a taxonomical nature, and that in fact charts and graphs are quite different things and therefore that neither one could be a more general case of the other.

Comment 2: Note that there are Bar Charts and there are Bar Graphs. also there are Pie Charts and there are Pie Graphs. These are not the same and they are in each case either charts or graphs according to the definitions given above.

Comment 3: Charts refer to tables or information contained in table-like formats. Charts are basically maps (in Greek 'chartis' means 'map'). Examples include taxonomies, such as the classification of animal groups, language families, or baseball teams. The purpose of a chart is to organize and display information by one or more categories or fields. All of the information in a chart is discrete (categorical) data. This means that the frequently used term 'flowchart' is basically flawed and it instead be 'flow-diagram'. Indeed, this is how some books refer to what is commonly known as 'flowchart'.

Diagrams

Definition: A diagram is the visualization of some specific operation of entities.

The basic types of diagrams are:

¨ Diagram of Apparatus: e.g. visualize the working of something, for instance a diagram depicting the working of an organization or of a device)

¨ Flow Diagram (or Block Diagram): e.g. visualize the sequence of tasks, for instance the sequential steps in a project. A Flow Diagram uses standard symbols to visualize tasks)

¨ Time Line Diagram: e.g. visualize the time for performing tasks, for instance the duration of each individual phase of a project)

Part 2: A second attempt (The role of Graphics in Instruction)

The University of Georgia – Athens

http://www.nowhereroad.com/cgl/chapter2/index.html

The three types of instructional graphics

Given the popularity and flexibility of graphics in instruction, a way is needed to make sense out of how they can be used to improve instructional materials. First, there is a need to describe the types of graphics commonly used in instruction. Second, there is a need to describe the various functions of each type when applied in an instructional or training setting. We will use a simple classification system that describes the types of visuals commonly used in instruction. These categories describe, in general, how graphics convey information and meaning, but do not speak directly to how they can be applied in instruction. Applying these graphics types to instruction is a separate issue and will be addressed later. The three types of graphics are classified as representational, analogical, and arbitrary (Alesandrini, 1984), as shown in Figure 2.1.

Representational Graphics

Representational graphics share a physical resemblance with the object they are supposed to represent. For example, a passage of text explaining the purpose and operation of a submarine probably would be accompanied by a picture of a submarine. Representational visuals range somewhere between highly realistic and abstract.

The most common examples of realistic representational visuals are photographs or richly detailed colored drawings, the latter of which are currently the highest quality images that can be generated on microcomputers. Multimedia systems present opportunities to incorporate near-photographic images, such as composite video images taken from videodisc or videotape players, or from computers with adequate memory. Although many would argue that the quality of these video images is much lower than photographs, the issue of representational integrity is largely a function of the context. For example, although most microcomputers could represent a realistic enough submarine for most purposes, the same quality would hardly suffice for an art lesson in which fine details of the Mona Lisa are featured and discussed. Actual photographic images can be made available in multimedia systems that integrate slide/tape projectors (Pauline & Hannafin, 1987).

Figure 2.1

The Three Types of Instructional Graphics

An example of an abstract representational visual is a line drawing. These also range in quality from richly detailed to rudimentary drawings. For example, Figure 2.2 shows an example of a passage explaining the use and function of an astronaut's space suit. While it is clearly a line drawing, it was produced from a photographic original. On the other hand, Figure 2.1 shows a rather crude drawing of a submarine. This primitive drawing still captures the most salient features of a submarine. In fact, the lack of interesting details and background makes it easier to focus on the essential characteristics of a submarine and far less likely to get confused or distracted by extraneous details. For these reasons, simple line drawings are often considered better learning aids than realistic visuals, especially when the lesson is externally paced, such as in films and video (Dwyer, 1978). The issue of realism will be discussed in more detail in chapters 5 and 7.

Figure 2.2

Snapshot of a CBI lesson using a presentation graphic consisting of a representational line drawing.

Analogical Graphics

The range of representational visuals is probably the most common type of illustration used in instructional materials today, including computer environments. However, presenting students with an accurate representation of something may not always be the best learning tool. One such example is when students have absolutely no prior knowledge of the concept. Instructional research indicates that analogies may be effective instructional strategies in such instances (Curtis & Reigeluth, 1984; Halpern, Hansen, & Riefer, 1990). For example, if students do not understand the idea that a submarine is able to dive under water, it might be more appropriate to first suggest that a submarine is analogous to a fish so students understand this characteristic. However, a better analogy would be a dolphin because it, like a submarine, must surface occasionally for air, or better yet, a whale, because of its size. Of course, a submarine is not a dolphin or a whale, so learners must understand that the analogy is being used only to represent similarities. Differences do exist, and it is important that students understand the analogy's limits.

Educational psychologists often describe learning as a process that goes from the known to the unknown (Reigeluth & Curtis, 1987). An analogy can act as a familiar "building block" on which a new concept is constructed (Tennyson & Cocchiarella, 1986). Of course, if the student does not understand the content of the analogy, then its use is meaningless and confusing. Worse yet, students may form misconceptions from an inadequate understanding of how the analogy and target system are alike and different (Zook & Di Vesta, 1991). The usefulness of the analogy, therefore, is largely dependent on the learner's prior knowledge. Graphics can help learner's see the necessary associations between parts of the analogy. An example of a not so subtle analogical graphic is shown in Figure 2.3. The organization that paid for this ad obviously believes that America's dependency on foreign oil is a big mistake and is like a bomb ready to go off. Whether or not you agree with this position does not detract from the obvious message that is being communicated with this graphic.

Figure 2.3

Example of an analogical graphic.

Arbitrary Graphics

Arbitrary graphics offer visual clues, but do not share any physical resemblances to the concept being explained. In a sense, this category acts as a "catch-all" for any graphic that does not offer any resemblance of real or imaginary objects, but yet contains visual or spatial characteristics that convey meaning. Examples range from the use of spatial orientations of text, such as outlines, to flowcharts, bar charts, and line graphs.

All information can be represented as existing on a continuum. At one end are the most concrete representations -- real objects. Nearby are highly realistic representational pictures. At the other end are spoken and written words that represent the most abstract form of communication. In the center of this continuum would be arbitrary graphics.

Charts and graphs are probably the most common types of arbitrary graphics (Winn, 1987). Charts refer to tables or information contained in table-like formats. Examples include taxonomies, such as the classification of animal groups, language families, or baseball teams (such as shown in Figure 2.4). The purpose of a chart is to organize and display information by one or more categories or fields. All of the information in a chart is discrete (categorical) data.

A "cognitive map" is an interesting example of a chart that has much support from research as a learning tool. Cognitive maps are part of an instructional technique called spatial mapping (Holley & Dansereau, 1984). The purpose of cognitive maps is to show graphically the relationships and hierarchies of related ideas and concepts. Figure 2.1 depicts a simple example of a cognitive map that shows how two concepts -- submarine and transportation -- are related. Each fact or concept is called a node and is connected to other nodes by links that indicate the relationship between the nodes. Often, these links are then labeled further to clarify the relationships between the connected nodes. Research has shown that these graphics tend to be most useful when the student constructs the map or when the map is constructed in front of the student, usually during the explanation of the ideas, rather than just providing a completed map to a student to study.

Similarly, graphs also logically represent information along one or more dimensions, but the main purpose of graphs is to show relationships among the variables in the graph, as shown in Figure 2.5. The most common types of graphs are line graphs and bar graphs, although many other types abound, such as pie graphs, scatterplots, etc. Another difference between charts and graphs is that at least one of the variables in a graph usually will be continuous. Continuous data contain an infinite number of points along a continuum. Height or weight are continuous variables. Someone's height may be reported as six feet, one inch, but this is just for convenience because height can never be measured exactly.

Figure 2.4

Example of presenting categorical information in a table.

The way space is used in a chart or graph to form sequences and patterns is very important. Research has shown that more rapid problem solving results from diagrams in which conceptual relationships are shown spatially, rather than by text (Win, Li, & Schill, 1991). In charts, the sequence of information is usually not a critical feature. For example, there are many ways to sequence the various names and hometowns of major league baseball teams. It doesn't really matter if the American League or National League is listed first or second. The teams are listed alphabetically in Figure 2.4, but changing this order does not change how information in the chart is conveyed.

The pattern of a chart is typically conveyed through row or column headings. The baseball chart is informational because of the primary and secondary groupings: a) American and National; and b) East and West. Also, the proximity of items to one another in a chart may also convey information. A chart that describes an animal family, such as marsupials, would show how much one group is related to another by how close the groups are located on the chart along one dimension.

The sequence of a graph is crucial to understanding the information it contains. For example, the usefulness of a graph that describes average monthly temperatures, such as those shown in Figure 2.5, would be seriously curtailed if it were arranged alphabetically by month instead of chronologically. "Reading" the graph is easier when the graph displays information in a natural sequence. Also, the purpose of a graph is usually to compare information across parts of the graph, such as which times of the year are the hottest or the coldest.

This also speaks to the importance of the pattern of information displayed in a graph. Consider Figure 2.5 containing three separate line graphs: one graph showing the monthly temperatures for both Houston and Pittsburgh, and then one superimposing the two graphs. Graphs such as these are meaningful if they convey trends and comparisons quickly at a glance. When superimposed, the line graphs quickly allow the reader to compare the climates of the two cities.

An effective and popular graph type is the time-series plot, where one axis is tied to some chronological variable, such as seconds, minutes, or years (Tufte, 1983). Scientists often use time-series plots to show how large and complicated data sets change over time. A simple example of the resulting motion of a bicycle's pedal as it turns while the bicycle moves forward at different speeds is shown in Figure 2.6. Of course, computer animation provides many opportunities for improving time-series plots, since the actual dynamics of the display over time could be shown and potentially controlled.

One of the most influential figures on how to visually display quantitative information has been Edward Tufte (1983). His most fundamental principle of statistical graphics is simply "above all else show the data" (Tufte, 1983, p. 92). Yet, it is amazing how often this simple principle is violated, sometimes unintentionally and sometimes deliberately to distort the data (such as for political motives). For this reason, Tufte defines the "lie factor of graphs" as the size of the effect shown in the graph divided by the actual size of the effect in the data. A lie factor of 1 denotes no lie, but ±.05 constitutes a substantial distortion of the data. Tufte (1983) also admonishes designers of graphs to keep "chartjunk," nonessential graphical decoration, to a minimum. Tufte feels that "the best designs are intriguing and curiosity-providing, drawing the viewer into the wonder of the data. . ." (p. 121).

Combining Characteristics of the Three Types of Graphics

It should be noted that graphics are frequently constructed to contain characteristics of two or more of the three graphic types. Representational and arbitrary graphics are often mixed, such as the use of arrows and labels superimposed on a drawing. Pict-o-graphs (or isotypes), another popular type of graph (especially in magazines and newspapers), overlap characteristics of representational and arbitrary graphics, as shown in Figure 2.7.

Figure 2.5

Examples of line graphs.

Figure 2.6

Three time-series plots showing the path that a bicycle's pedal follows as the bicycle moves forward, given different gear ratios.

Figure 2.7

Examples of "pict-o-graphs."

The overlay of representational and arbitrary graphics onto geographical maps is one of the oldest mixtures of graphical forms. One of the most striking examples is the map drawn by the French engineer Charles Joseph Minard in 1861 to show the tremendous losses of Napoleon's army during his Russian Campaign of 1812. The map, shown in Figure 2.8, is best described by Tufte (1983):

Conclusion

The way the terms Diagram, Graph and Chart are used and/or defined today is in many cases flawed.

In many cases, ‘diagrams’ is used as the most general term in graphical data representation. Strictly this is not correct. However, it is generally accepted and often regarded as correct by respected dictionaries.

Graphical representations of data should be judged on an individual basis according to the criteria and definitions given above and only then appropriately termed as graphs, charts or diagrams. What seems appropriate or correct may not be so upon closer inspection.

About Diagrams, Graphs and Charts

Intro