Graphs paper types

When we draw a scatter plot of all X versus Y data, we see that some sort of shape can be described by the data points. From the scatter plot we can take a basic guess as to which type of curve will best describe the X—Y relationship. To aid in the decision process, it is helpful to obtain scatter plots of transformed variables. For example, if a scatter plot of log Y versus X shows a linear relationship, the equation has the form of number 6 above, while if log Y versus log X shows a linear relationship, the equation has the form of number 7. To facilitate this we frequently employ special graph paper for which one or both scales are calibrated logarithmically. These are referred to as semilog or log-log graph paper, respectively. 

A graph paper based on this type of relationship can be obtained. It permits convenient graphical representation of size distribution data (as shown in Fig 3) even if the distribution does not follow a log-probability relationship. In addition, the assumption of a log-probability distribution as an approximation permits simple conversion from one basis of representing size distribution, mean size, or median size to another basis... 

The solid line typifies the shape of curve shown by actual materials on this type of plot. If a material obeys a log-probability relationship, the piot on this graph paper is a straight line, as... 

Lets take a step back and look at the process. Say that we are plotting a simple scatter plot of some X,Y pairs. The first step is to pick a suitable graph paper, there are a lot of them, different types and scales - someone else has gone through the trouble of working out the rulings, line thickness and such and... 

The solid line typifies the shape of curve shown by actual materials on this type of plot. If a material obeys a log-probability relationship, the plot on this graph paper is a straight line, as shown by the two dashed lines, and can be completely characterized by two numbers (1) a median diameter, corresponding to the 50% cumulative size, and (2) a standard geometric deviation, a number equal to or greater than unity that is the ratio of the 84.13% to the 50% or the 50% to the 15.87% cumulative size... 

Homogeneous EIA lend themselves better to dose-response curve linearization than solid-phase EIA. This type of EIA is generally used for the determination of concentrations of small molecules (haptens, drugs). The major supplier of this type of EIA kits (Syva Co.) recommends the plotting of the response variable ( EMIT Units ) vs the log of the concentration or the presentation of the results on special non-linear graph paper provided by them, which is, in fact, logit-log paper. 

Another type of special ratio is scale. Create a scale drawing of the floor plan of your home. Use an appropriate scale, a ruler, and graph paper to help you be accurate. Calculate the total square footage of your house, and find out what percentage your room is to the rest of the house. 

To simplify plotting of the data as shown in Figure 5, special log-probability graph paper is used. As an example, the data shown in Table 8 have been plotted on this type of graph paper in Figure 7, while erg has been calculated from ... 

The rate law can now be used in the design of an industrial CSTR. For those wl prefer to find k using semilog graph paper, this type of analysis is given in Chapter Summary Note.s on the CD-ROM. An Excel tutorial is also given in the Summa Notes for Chapter 3. 

Beside bioburden, the other determinant of sterility assurance is the survival curve and its shape and its slope. It is not correct to assume that all survival curves are of the simple linear type when data is plotted on semilogarithmic graph paper. Three general types of survival curve have been reported, the exponential curve, the shouldered" curve, and the "tailed" curve (Fig. 4). 

If no satisfactory fit can be obtained by using any of these suggestions, the analyst should try more complicated functions. Plotting the data on special kinds of graph paper, such as reciprocal or probability paper may be helpful. After the type of function is found, the constants associated with it are determined by a least-squares fit (see Sec. 11.4). 

Four types of graph paper are commonly used for plotting particle size distributions, depending on the sort of information that is required (a) ordinary... 

Special double logarithmic graph paper suitable for this type of plotting is available and the data from Table 2.14 are shown on such a plot in Figure 2.18b. From this plot it is possible to determine the 16, 50 and 84% cumulative percentages needed to calculate the MS/CV, as described above. Alternatively, the distribution can be characterized by the uniformity factor, n. In the example shown the median size = 870 pm (the same as determined in Figure 2.18a), the statistical mean size d = 1000 pm, and the uniformity factor n= 1.8. 

Plot the data given in (A), (B), and (C) to determine the functional relation between the two variables. That is, obtain an equation to express the second variable as a function of the first variable. Each set of data will yield a straight line when plotted on one of three types of graph paper - normal, semilog, or log-log. (See Appendix D.)... 

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