graph

Algebra

(noun)

A diagram displaying data, generally representing the relationship between two or more quantities.

Related Terms

  • point
  • equation
  • dependent variable
  • independent variable
  • expression

(noun)

A diagram displaying data; in particular, one showing the relationship between two or more quantities, measurements or numbers.

Related Terms

  • point
  • equation
  • dependent variable
  • independent variable
  • expression
Statistics

(noun)

A diagram displaying data; in particular one showing the relationship between two or more quantities, measurements or indicative numbers that may or may not have a specific mathematical formula relating them to each other.

Examples of graph in the following topics:

  • Graphing skill

  • Graphing on Computers and Calculators

    • They can be created with graphing calculators.
    • Graphs are often created using computer software.
    • GraphCalc includes many of the standard features of graphing calculators, but also includes some higher-end features.
    • c) Three-dimensional graphing: While high-end graphing calculators can graph in 3-D, GraphCalc benefits from modern computers' memory, speed, and graphics acceleration.
    • It also includes tools for visualizing and analyzing graphs.
  • Misleading Graphs

    • In statistics, a misleading graph, also known as a distorted graph, is a graph which misrepresents data, constituting a misuse of statistics and with the result that an incorrect conclusion may be derived from it.
    • Misleading graphs are often used in false advertising.
    • Generally, the more explanation a graph needs, the less the graph itself is needed.
    • Graphs may also be truncated to save space.
    • In the United States, graphs do not have to be audited.
  • Simplex or multiplex relations in the graph

    • The friendship graph (figure 3.2) showed a single relation (that happened to be binary and directed).
    • The spouse graph (figure 3.3) showed a single relation (that happened to be binary and un-directed).
    • Figure 3.4 combines information from two relations into a "multiplex" graph.There are, potentially, different kinds of multiplex graphs.
    • We graphed a tie if there was either a friendship or spousal relation.
    • But, we could have graphed a tie only if there were both a friendship and spousal tie (what would such a graph look like?
  • Graphing Quantitative Variables

    • There are many types of graphs that can be used to portray distributions of quantitative variables.
    • The upcoming sections cover the following types of graphs: (1) stem and leaf displays, (2) histograms, (3) frequency polygons, (4) box plots, (5) bar charts, (6) line graphs, (7) scatter plots, and (8) dot plots.
    • Some graph types such as stem and leaf displays are best-suited for small to moderate amounts of data, whereas others such as histograms are best-suited for large amounts of data.
    • Graph types such as box plots are good at depicting differences between distributions.
  • Graphing the Normal Distribution

    • The graph of a normal distribution is a bell curve, as shown below.
    • Out of these two graphs, graph 1 and graph 2, which one represents a set of data with a larger standard deviation?
    • The correct answer is graph 2.
    • The larger the standard deviation, the wider the graph.
    • The smaller it is, the narrower the graph.
  • Introduction to kinds of graphs

    • Now we need to introduce some terminology to describe different kinds of graphs.
    • Figure 3.2 is an example of a binary (as opposed to a signed or ordinal or valued) and directed (as opposed to a co-occurrence or co-presence or bonded-tie) graph.
    • Figure 3.3 is an example of a "co-occurrence" or "co-presence" or "bonded-tie" graph that is binary and undirected (or simple).
    • Figure 3.4 is an example of one method of representing multiplex relational data with a single graph.
  • Line Graphs

    • Judge whether a line graph would be appropriate for a given data set
    • A line graph is a bar graph with the tops of the bars represented by points joined by lines (the rest of the bar is suppressed).
    • A line graph of these same data is shown in Figure 2.
    • Although bar graphs can also be used in this situation, line graphs are generally better at comparing changes over time.
    • A line graph of the percent change in the CPI over time.
  • Visualizing Domain and Range

    • The domain and range can be visualized using a graph, such as the graph for f(x)=x2f(x)=x^{2}f(x)=x​2​​, shown below as a red U-shaped curve.  
    • The range for the graph f(x)=−112x3f(x)=-\frac{1}{12}x^3f(x)=−​12​​1​​x​3​​, is R\mathbb{R}R.
    • The graph of f(x)=x2f(x)=x^2f(x)=x​2​​ (red) has the same domain (input values) as the graph of f(x)=−112x3f(x)=-\frac{1}{12}x^3f(x)=−​12​​1​​x​3​​ (blue) since all real numbers can be input values.  
    • The range of the blue graph is all real numbers, R\mathbb{R}R.
    • Use the graph of a function to determine its domain and range
  • Graphs of Logarithmic Functions

    • Below is the graph of the y=logxy=logxy=logx.
    • The graph crosses the xxx-axis at 111.
    • That is, the graph has an xxx-intercept of 111, and as such, the point (1,0)(1,0)(1,0) is on the graph.
    • Of course, if we have a graphing calculator, the calculator can graph the function without the need for us to find points on the graph.
    • In fact if b>0b>0b>0, the graph of y=logbxy=log{_b}xy=log​b​​x and the graph of y=log1bxy=log{_\frac{1}{b}}xy=log​​b​​1​​​​x are symmetric over the xxx-axis.
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