graph

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

• Graphs of Logarithmic Functions

  • Below is the graph of the $y=logx$.
  • The graph crosses the $x$-axis at $1$.
  • That is, the graph has an $x$-intercept of $1$, and as such, the point $(1,0)$ 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 $b>0$, the graph of $y=log{_b}x$ and the graph of $y=log{_\frac{1}{b}}x$ are symmetric over the $x$-axis.