supl004 - 173 Supplement SUPL- 004 004 supplement Some...

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173 Supplement SUPL- 004 Some Comments about Graphing SUPL-004 Graphs are an important means of displaying both experimental data and computed quantities. T e presentation of data in a graph often permits regularities, or irregularities, in data to be discerned more easily than by an examination of the same data in a table. Consider the following example: T e density of solutions of glycerol in water is measured as a function of the weight fraction of glycerol in the solution. ±able 4-1 shows the results of the measurements. Table 4-1. WT FRACTGLYCEROL 0.00 0.12 0.24 0.39 0.48 0.64 0.78 0.89 0.99 DENSITY 1.008 1.016 1.033 1.055 1.113 1.108 1.138 1.170 1.199 &YBNJOBUJPO!PG!UIF!UBCMF!TIPXT!B!EFm !OJUF!JODSFBTF!PG!EFOTJUZ!XJUI!JODSFBTJOH!GSBDUJPO!PG!HMZDFSPM!JO!UIF! solution, but the detailed nature of that dependence is not apparent. Does the density increase linearly (in direct proportion) with weight fraction or in some other way? An examination of the same data plotted in a graph (Figure 4-1) shows that the dependence exhibits a clear curvature. It also highlights the irregularity of the measured density at a weight fraction of glycerol of 0.48. Prepared by R. F. Schneider (Rev 3/09) supplement
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174 Supplement SUPL- 004 0.00 0.20 0.40 0.60 0.80 1.00 0.9 1.0 1.1 1.2 1.3 Weight Fraction of Glycerol Density (g/mL) DENSITY OF WATER GLYCEROL SOLUTIONS A graph of the data in Table Figure 4-1. 4-1 What are the components of a graph? Figure 4-2 shows the more important objects UIBU!DPOTUJUVUF!B!TDJFOUJmD!HSBQI!)XF!DPOTJEFS!POMZ!3.EJNFOTJPOBM!HSBQIT!GPS!UIF!NP - ment). A title is certainly desirable to advise a reader what the graph is all about. ±e axes of a graph are normally called the abscissa (the horizontal axis) and ordinate (the vertical axis) as shown. In place of the words “abscissa” and “ordinate,” a graph should include labels that describe the quantities that are being displayed. Along with the labels should be the units in which the quantities are measured. ±e body of the graph consists of a grid of lines which may or may not be displayed. ±ere are typically data points (which we represent as bullets for the moment) to show the quantities that were actually measured. Normally, there is a line which may be straight or may be curved, as in the example. ±e line shows the values that would be expected if measurements were made at each point between the actual experimental measurements. ±e lower left corner of the grid is normally called the origin of the graph. 0 01234567891 0 1 2 3 4 5 6 Abscissa - Units Independent Variable Ordinate - Units GRAPH TITLE Origin Data points Graph components Figure 4-2.
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175 Some Comments about Graphing Te construction of graphs requires the application of some commonsense principles. Tese arise largely out of considerations of the ultimate use of the graph. If the graph is intended to show only gross qualitative behavior of the variables, little detail needs to be shown (e.g., see Figure 4-3). If the objective of a graph is to permit quantitative conclusions to be drawn, the graph must be constructed to facilitate this process for the end user (Figure 4-1 is such an example).
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supl004 - 173 Supplement SUPL- 004 004 supplement Some...

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