The purpose of a graph is to visually depict a set of data in a manner that all of the data can be viewed simultaneously and quickly processed by the interpreter. A graph is typically presented on a two dimensional medium and therefore the simplest graphs to interpret that require the least specialized training for both the presenter and the viewer are also constructed in two dimensions. Some graphs may be three dimensional, such as stereo nets, but do to the complexity of providing a graphing system of three dimensions on two dimensional portable medium, special training is required to produce and interpret such a graph so these communications are typically not as widely distributed as the much more universally applied two dimensional graphs.
A two dimensional graph is typically constructed on a pair of perpendicular axes, one oriented in the vertical direction, the other oriented in the horizontal direction; which correspond to the Cartesian coordinate system as the ‘y-axis’ and the ‘x-axis’, respectively. Where the two axes intersect is referred to as ‘the origin’ of a Cartesian plane. The Cartesian convention allows for negative values to left and to the downward side of the origin along these two axes and absolute or positive values to the right and vertically upward of the origin.
Thus data from a set of data in a table, or functional values from mathematical formula’s render well on a Cartesian system. A visual survey of all the data simultaneously plotted on a Cartesian plane allows the viewer to detect patterns, trends, anomalies, and other data and functional characteristics in this presentation that would be less recognizable if it were presented as a list or in table format. It is for this reason that line graphs and bar graphs are a popular medium for portraying raw data stored in tables.
A bar graph positions each record along the horizontal axis according to criteria that is depicted as a label on the axis. The positioning of data in the horizontal denotes a sorting order. For example, the time stamp of the record might be used to determine the records position on the horizontal dimension and then that axis would be labeled as ‘time’ or ‘date’. If temporal positioning is being graphed, it will almost always be depicted in the horizontal, as per convention. The spacing of data on a bra graph is typically at discreet points along the axis and the display is typically not proportioned, but there are occasional exceptions.
The vertical axis of a bar graph is used to denote magnitude and will be labeled accordingly. It is most often linear and one to one with the data values in the table but occasionally if a dataset contains wide disparities in magnitude values the graphic may use a logarithmic scale in the vertical direction. This will often depend on the natural properties of the objects, or elements, that are being graphed. Most financial data, such as weekly sales, would appear as a linear value whereas scientific data may be more presentable in logarithmic.
A line graph may be generated from a bar graph by simply connecting all of the endpoints of a bar graph to their neighbors. A line graph is often generated by a data table containing more data elements than is desirable for a bar graph and can reduce clutter. But the most important advantage of a line graph is that it adds additional functionality than a bar graph might imply but does not directly depict. A line graph visually depicts rate in the slope of the line that connects the data elements and the area contained under the line represents a summation of the whole dataset. Even though the data elements are presented in two dimensions and each element only contains two free parameters, the graph is capable of communicating a detailed storyline with the right set of data, and is hence very popular in a multitude of fields.
Another popular two-dimensional graph worth mentioning is the pie chart. The pie chart does not make use of the Cartesian axial system but rather incorporates a circle with the origin at its geometric center. Ordinarily a pie chart is used when all the data represents a portion of a whole quantity which when added up is equal to one hundred percent of the whole. The quantity in question is thus divided up according to its identifiable parts and graphed as a proportional quantity of a circle. Two lines forming an angle are drawn from the origin to the circumference of the circular field forming the so-called “pie slice” for each “piece” of the whole. The pie chart is one of the easiest charts to read but is very difficult to draw, because to portray the piece of the whole properly, one must know the angle of the two lines emanating from the origin. Most pie charts do not deal with a sorting order as do the bar and line charts, but a sorting order is available if one were to plot the pieces in the clockwise direction.
One of the great advantages of two-dimensional graphing systems is their portability, utility, and ease of use. It is interesting to think that if one had a multitude of pie charts that were somehow sortable and had varying properties of magnitude, that each the pie charts could be plotted as a single element on a Cartesian system.
What if one had weekly sales data from a department store and at different times of the year some departments did better than other?
Mothers Day vs. Labor Day?
Click the point on the line graph and, tada! A pie chart!