Graphs common types

Although spherical vessels have a limited process application, the majority of pressure vessels are made with cylindrical shells. The heads may be flat if they are suitably buttressed, but preferably they are some curved shape. The more common types of heads are illustrated on Figure 18.16. Formulas for wall thicknesses are in Table 18.3. Other data relating to heads and shells are collected in Table 18.5. Included are the full volume V0 and surface S as well as the volume fraction V/V0 corresponding to a fractional depth H/D in a horizontal vessel. Figure 18.17 graphs this last relationship. For ellipsoidal and dished heads the formulas for V/V0 are not exact but are within 2% over the whole range. 

The correct answer is (A). In an exothermic reaction, the potential energy of the products will be lower than that of the reactants. The energy difference is due to the loss of energy as heat. The only graph that shows a decrease in the energy of the products is choice (A). The other most common type of plot is choice (B), which represents an endothermic reaction. 

The curve on a graph gives a great deal of information about the relationship between the variables. Four common types of curves are shown in Figure 15. Each type of curve corresponds to a mathematical relationship between the independent and dependent variables. 

After organizing data in tables, scientists usually want to display the data in a more visual way. Using graphs is a common way to accomplish that. There are three common types of graphs—bar graphs, pie graphs, and line graphs. 

Scatter plots are the most common type of graph used to show relationships between a dependent variable (responses) and independent variables (factors). Judiciously selecting and sizing the symbols in scatter plots allows one to communicate trends and the measured values associated error. Frequently, to show the effect of more than one independent variable, different symbol types or colors can be used. Three-dimensional plots, surface plots, and contour plots are becoming more common to illustrate the effect of two or more factors on the dependent variable. Bar charts (and pie charts) are popular for presentations, and histograms are useful to compare the distribution of populations. Ternary plots are used in thermodynamics and to demonstrate explosion limits of different compositions of gases. 

A graph is often the most convenient way to present or display a set of data. Various kinds of graphs have been devised, but the most common type uses a set of horizontal and vertical coordinates to show the relationship of two variables. It is called an x-y graph because the data of one variable are represented on the horizontal or x-axis (abscissa) and the data of the other variable are represented on the vertical or y-axis (ordinate). See Figure I.l. 

Common clinical trial graphics are the focus of this chapter. First, we discuss the types of graphs that are most often encountered in clinical trial analysis and reporting. Then we examine the various tools that SAS provides to help produce these graphs. Sample graph programs are provided to show how many of these graphs can be produced. 

There are several types of graphs that are common to clinical trial analysis and reporting. What follows are some brief descriptions of these graphs. 

Statistics is a branch of mathematics that involves the study of data. Probability is the study of chance. This chapter will refresh your understanding of common statistical measures, graphs, and probability. Before proceeding to the lesson, take this ten-item Benchmark Quiz to see how much you remember about statistics and probability. These questions are similar to the type of questions that you will find on important tests. When you are finished, check the answer key carefully to assess your results. Your Benchmark Quiz analysis will help you determine how much time you need to spend on statistics and probability, and the specific areas in which you need the most careful review and practice. 

Keep the format simple. When possible, use headings, lists, and other ways of breaking up the text. You can use capital letters for emphasis, but don t type an entire message in all caps—it s hard to read, and it s commonly considered virtual shouting. Other formatting, such as italics, bullets, tables, and graphs, can be lost in an e-mail message. 

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