Difference between revisions of "Graph"
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==Definitions== | ==Definitions== | ||
*1: the collection of all [[points]] whose coordinates satisfy a given relation (as a function) | *1: the collection of all [[points]] whose coordinates satisfy a given relation (as a function) | ||
*2: a diagram (as a series of one or more points, lines, line segments, curves, or areas) that [[represents]] the variation of a [[variable]] in comparison with that of one or more other variables | *2: a diagram (as a series of one or more points, lines, line segments, curves, or areas) that [[represents]] the variation of a [[variable]] in comparison with that of one or more other variables | ||
| − | *3: a collection of [ | + | *3: a collection of [https://en.wikipedia.org/wiki/Vertices vertices] and edges that join pairs of vertices |
==Description== | ==Description== | ||
A '''graph''' is pictorial [[representation]] of [[statistical]] [[data]] or of a functional [[relationship]] between [[variables]]. Graphs have the [[advantage]] of showing general tendencies in the [[quantitative]] behavior of data, and therefore serve a [[predictive]] function. As mere approximations, however, they can be inaccurate and sometimes misleading. | A '''graph''' is pictorial [[representation]] of [[statistical]] [[data]] or of a functional [[relationship]] between [[variables]]. Graphs have the [[advantage]] of showing general tendencies in the [[quantitative]] behavior of data, and therefore serve a [[predictive]] function. As mere approximations, however, they can be inaccurate and sometimes misleading. | ||
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If the independent variable is not expressly [[temporal]], a bar graph may be used to show discrete [[numerical]] quantities in relation to each other. To [[illustrate]] the relative [[populations]] of various nations, for example, a series of [[parallel]] columns, or bars, may be used. The length of each bar would be [[proportional]] to the size of the population of the respective country it represents. Thus, a demographer could see at a glance that China’s population is about 30 percent larger than its closest rival, India. | If the independent variable is not expressly [[temporal]], a bar graph may be used to show discrete [[numerical]] quantities in relation to each other. To [[illustrate]] the relative [[populations]] of various nations, for example, a series of [[parallel]] columns, or bars, may be used. The length of each bar would be [[proportional]] to the size of the population of the respective country it represents. Thus, a demographer could see at a glance that China’s population is about 30 percent larger than its closest rival, India. | ||
| − | This same [[information]] may be [[expressed]] in a part-to-whole [[relationship]] by using a circular graph, in which a [[circle]] is divided into sections, and where the size, or angle, of each sector is directly proportional to the percentage of the whole it represents. Such a graph would show the same [[relative]] population sizes as the bar graph, but it would also [[illustrate]] that approximately one-fourth of the world’s population resides in China. This type of graph, also known as a [ | + | This same [[information]] may be [[expressed]] in a part-to-whole [[relationship]] by using a circular graph, in which a [[circle]] is divided into sections, and where the size, or angle, of each sector is directly proportional to the percentage of the whole it represents. Such a graph would show the same [[relative]] population sizes as the bar graph, but it would also [[illustrate]] that approximately one-fourth of the world’s population resides in China. This type of graph, also known as a [https://en.wikipedia.org/wiki/Pie_chart pie chart], is most commonly used to show the breakdown of items in a [[budget]]. |
| − | In [ | + | In [https://en.wikipedia.org/wiki/Analytic_geometry analytic geometry], graphs are used to map out functions of two [[variables]] on a [https://en.wikipedia.org/wiki/Cartesian_coordinates Cartesian coordinate system], which is composed of a [[horizontal]] x-axis, or abscissa, and a [[vertical]] y-axis, or ordinate. Each axis is a real number line, and their [[intersection]] at the zero point of each is called the [[origin]]. A graph in this sense is the locus of all points (x,y) that satisfy a particular function. |
[[Category: Mathematics]] | [[Category: Mathematics]] | ||
Latest revision as of 00:26, 13 December 2020
Definitions
- 1: the collection of all points whose coordinates satisfy a given relation (as a function)
- 2: a diagram (as a series of one or more points, lines, line segments, curves, or areas) that represents the variation of a variable in comparison with that of one or more other variables
- 3: a collection of vertices and edges that join pairs of vertices
Description
A graph is pictorial representation of statistical data or of a functional relationship between variables. Graphs have the advantage of showing general tendencies in the quantitative behavior of data, and therefore serve a predictive function. As mere approximations, however, they can be inaccurate and sometimes misleading.
Most graphs employ two axes, in which the horizontal axis represents a group of independent variables, and the vertical axis represents a group of dependent variables. The most common graph is a broken-line graph, where the independent variable is usually a factor of time. Data points are plotted on such a grid and then connected with line segments to give an approximate curve of, for example, seasonal fluctuations in sales trends. Data points need not be connected in a broken line, however. Instead they may be simply clustered around a median line or curve, as is often the case in experimental physics or chemistry.
If the independent variable is not expressly temporal, a bar graph may be used to show discrete numerical quantities in relation to each other. To illustrate the relative populations of various nations, for example, a series of parallel columns, or bars, may be used. The length of each bar would be proportional to the size of the population of the respective country it represents. Thus, a demographer could see at a glance that China’s population is about 30 percent larger than its closest rival, India.
This same information may be expressed in a part-to-whole relationship by using a circular graph, in which a circle is divided into sections, and where the size, or angle, of each sector is directly proportional to the percentage of the whole it represents. Such a graph would show the same relative population sizes as the bar graph, but it would also illustrate that approximately one-fourth of the world’s population resides in China. This type of graph, also known as a pie chart, is most commonly used to show the breakdown of items in a budget.
In analytic geometry, graphs are used to map out functions of two variables on a Cartesian coordinate system, which is composed of a horizontal x-axis, or abscissa, and a vertical y-axis, or ordinate. Each axis is a real number line, and their intersection at the zero point of each is called the origin. A graph in this sense is the locus of all points (x,y) that satisfy a particular function.
