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Graphing and the Visual
Presentation of Data Part 1: Introduction
and Basics Please note that this section is still in development. Types The type of plot needed will depend heavily, though not exclusively, on the data. This requires the author to have an initial understanding of their data, even though this understanding is expected to develop. In this section we review several types of plots and for what types of situations they are used.
X-Y scatter - simple, any raw format of data may be plotted. This format is useable for most plots, and is necessary when the x-axis data are not consistently spaced--whether the intervals be variable or random.
Bar - Not particularly useful for a single series of data (unless particularly easy viewing is desired), this type really comes into its own when comparing several items in different (related or not) catagories. Sometimes the area of the bars is used to depict comparisons. In such cases, it is important to decide if the Y-axis is measured from zero or not. Here we see the age distribution by sex in the 1983 US populaton. Separating the sexes reveals a disparity in trends which would be hidden if the two were combined. Note that the population (for women) can not be negative on the x-axis...the undesired persistence of the negative to the left of zero is a limitation of the program used. (61+) column types: simple, connected, grouped, subdivided, floating,
deviation (from average), rande (like floating)
Line- The Line type is used when the units on the X-axis are constant-- time (sample interval rate), linear progression of any unit (1 meter, 2m, 3m, ...), et cetera. The Line graph type is also used when no X-axis numbers are needed or the axis carries no numerical meaning, as in the case of categories in the the graph below. (68+) line types: "step", line, surface, multi-surface
(plotted in absolute #s), mmulti-surface 100% chart (plotted in %s), band
chart (ie, difference between cost and revenue plots, use different colors).
last is also known as a an intersecting band chart [example of polar graph] Polar / Spherical - This type is used in systems involving degree-based oreintation, for example, effect of wind direction on a sailboat heading North. Spherical graphs are seldom seen, but are the 3-D extension of the polar graph. [example of surface graph - matrix calculations?] Surface / 3-D - Surface graphs are very useful in complex and multi-variable systems, notably matrix math. 3-D graphs are , high-order equations Multi-axis - Multi-axis graphs are quite difficult to mimic in Excel. They can, however, be quite useful when comparing two series (more is easily confusing) on the same X-axis. For example, we could take the Tin-Bismuth alloy system composition (0 to 100% Tin and the reverse for Bismuth) and plot melting temperature on the left Y-axis and Ultimate Tensile Strength (UTS) on the right Y-axis. This would permit easy comparison of two properties of this alloy system on the same graph.
Sub-types Cumulative Used to show change in rate of growth
Percentage used to show ratios to the whole. The two main variations are "pie" and "line". A pie chart shows a percentage breakdown at a single point in time. A pair or triplet of pie charts effectively used can show dramtatic changes. For more subtle or long-running changes, a line plot should be used. It must be noted, though, that in either type of plot the overall pool available has an effect on the message conveyed (or distorted). (91) percentages change over time...be clear in your reference! 500 to
400 = -20%, 400 to 300 = -25%, 500 to 300 = -40% (2 * -20% of original
amount)
For example, let us say that 5 companies possess equal market share of financial software installations in 2000 and at a point later in time (2005) the overall market size increases (due to customers new to the market). Let us further say that company A has 50,000 customers in 2000 (20% market share), and the market doubles to 500,000 customers by the year 2005. If company A maintains 50,000 customers and the other companies gain the new 250,000 customers, while their absolute size and market presence has not changed, their percent market share has--they are now down to 10% in the new market size.
Area / Differential - Fundamentally just a Line or X-Y plot with the area between the plot and the axis filled in, this plot type is used for quick reference and conveyance. In the case of a differenctial graph, the areas between 2 or more plots are filled in to show differences, not the area between the plots and the x-axis. In Net revenues for Pipe Fittings, Inc., the red differential bars indicate costs exceeded revenues, and black indicates revenues exceeded costs.
Running Average / Predictive Log or Log--Log - When the data for multiple plots varies or is separated by over an order of magnitude, it can be very difficult to depict trends on a normal X-Y or Line graph. In such cases, it is ususally prudent to convert one or both axes to a Logarithm axis, as is appropriate for each axis. Log and Log-Log plots can also be used (independantly and) with other functions--such as 1/x--to convert exponential and asymptotic trends to linear format. Then simple trendlines and calculations may be applied for determining trends and equation fit. This is especially usefull in programs which are more spreadsheet than graphing package. Others - A quick note about Excel and other graphing software. A couple programs with highly automated "wizards" have extensive libraries of different "graphs" and "types". Several of these extra options are rarely used, and a number of them are useless stylistic variaitons of one of the basic graph types. Leave these variations in the same place we left font effects...the dustbin. Part 4: Putting the Graph Together
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