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Unformatted text preview: 164 Sometimes referred to as a plot. A graph is a chart that graphically displays quantitative
relationships between two or more groups of information — for example, the relationship
between cities and their populations, a car's speed and its efficiency, or the buying power of
a dollar over time.  Graphs have combinations of one, two, or three straight or circular axes .
utilizing one or more quantitative scales. This deﬁnition clearly differentiates graphs from
other charts such as diagrams, tables, text charts, proportional charts, illustration charts, and
most maps. In a few cases there is a slight overlap between graphs and certain three
dimensional statistical maps, which may be called either a graphs or maps. Since graphs
constitute one of the major categories of charts, graphs are frequently referred to as charts.
Graphs offer many important features, a few of which are: ﬂ Large amounts of information can be conveniently and effectively reviewed — Overall patterns of data stand out more clearly than in tabulated form — Deviations, trends, and relationships many times are more noticeable — Comparisons and projections can many times be made more easily and accurately — Anomalies in data frequently become obvious — Viewers can more rapidly determine and absorb the essence of the information — When used in presentations, graphs shorten meetings and expedite group decisions
The following pages discuss the overall aspects of graphs. Detailed information is present
ed under individual graph headings and under headings that encompass families of graphs. Methods for categorizing graphs
Graphs are categorized several different ways, each focusing on one of their many facets.
Shown on this and the following pages are five methods used to categorize the major
graphs in use today. The graphs included in each category are quite subjective. ‘ Detailed
information on each category as well as on individual graphs are included under their
separate headings. Categorized by major family or configuration Most graphs can be categorized into one or more of the families or configurations shown
below. There is considerable overlapping. For example, a polar vector graph could be
included in the vector, circular, and/or line graph family.  Within each graph family there
are generally several major subcategories. For instance, in the column graph family, there
are subcategories of simple, grouped, overlapped, stacked, ﬂoating, range, difference,
deviation, pictorial, and progressive column graphs.  In some cases, specialized graphs are
constructed by combining features from two or more families of graphs. Line graph Area graph Column graph W '92 '93 ‘94 '95 '96 Polar graph Vector graph Nomograph
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Unlilled contour graph Filled contour graph Lined surface Fllled surlace (continued) Methods for categorizing graphs (continued) Categorized by area or ﬁeld in which the graph is used Three primary usage categories sometimes referred to in literature and software
applications are technical/scientific, data analysis (statistical), and business, though they are
seldom clearly defined. The examples shown below are representative of the types of
graphs included in these categories. Standard graphs such as line, column, and bar are not
included, since they are applicable to all categories. The categories into which graphs are
placed is subjective, with considerable overlap. For example, histograms are used by data
analysts, technical, and business personnel and therefore histograms could have been placed
in any, or all, of the three categories. Technical/scientiﬁc graphs These graphs are many times very specialized and often have a higher percentage of three—
dimensional graphs than either of the other two categories. Large amounts of data are
common and the data is frequently entered via equations or directly from electronic data
collection devices (sometimes referred to as real time data). 6 10a
Polargraph Wire frame graph Contour graph VectorEraph Surface graph Data analysis graphs (sometimes referred to as statistical) These graphs are used for such things as determining whether meaningful relationships
exist between various data, how the data is distributed, whether or not differences are
signiﬁcant, etc. 20 15 10 5 ,_,_, ' L (”L' ' .2 ;..‘.. n
D 02 0“ 05 013110 ' m o 2 4. e a 10 1 3 s 7 a n 1315
Quantile graph Probability graph Scatter graph Histogram Business graphs Business graphs sometimes fall into the following three major categories.  Analyzing and planning 1 12% 10
108%
104%
100% 100%
96% 92% . 1930 1991 D 2 4 5 8 10 Quantity A B c o a F Index graph Bubble graph Supply and demand Spider graph Pareto graph
graph 18 A 10 ' 100
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Vertical line graph Deviation graph Moving average graph Control graph Highlowclose graph  Presentation — Although used by all disciplines, presentation graphs are frequently
classified as business graphs. There are no special types of graphs in this
category, only variations of graphs in other categories with special emphasis on aesthetics, ease of understanding, and a focused message. 165 Methods for categorizing graphs (continued) Categorized by type of data plotted
Original data 1.000 These graphs are constructed with data in its unmodified form. 2 8°“ Many times the data is empirical, such as number of people, § 5°“ temperature, pressure, sales, income, defects, or salaries: things E :2: that can be observed or measured. The majority of graphs are based 0 on this type of data. 0 ﬁgmp‘lsgamfg BO
Scatter graph Derived data
Examples of graphs plotted from derived data are index, ratio,
deviation, residual, difference, change, and relative value
graphs. Derived data is generated by mathematically
manipulating original data. For example, index values may be
derived by dividing all values by a common reference value.
Deviation values are derived by subtracting some reference value, such as budget, from the actual values. Derived 1nd9x graph
data generally can not be observed or measured directly, although sometimes it is more meaningful than the original data. For example, when comparing crime in various cities,
total crimes are generally not as meaningful as crimes per thousand inhabitants. Abstract data Abstract graphs are generally used to illustrate such things as
concepts, principles, theories, or generalities. For example, an abstract
graph such as a breakeven graph is many times used to show how
sales, volume of product, and costs interrelate to generate a profit or
loss. The axes generally have titles but minimal or no labels. Since
these graphs often do not have a true quantitative scale, some people
prefer to call them charts or diagrams. Breakeven
«at Dollars Volu me
Breakeven graph ‘ Categorized by the number of axes Most graphs are either rectangular, circular, or triangular. With few exceptions, graphs
have one, two, or three primary axes depending on their geometric shape, or in a few cases,
the type of scales. The table below indicates the primary axes for each of the major
geometric conﬁgurations. See Axis, Graph. Australia Israel Malta Guatemala Circle graph Polar graph Not applicable Not applicable Graph (continued) Methods for categorizing graphs (continued) Categorized by purpose Analyzing, exploring, planning, etc. — Major focus is on extracting the information contained in the data so that meaningful
observations can be made, conclusions reached, andfor plans made. — Almost every form of graph is used in these types of applications except those
specifically designed for presentation or publication purposes, such as pictorial graphs. — Graphs that compare multiple sets of data such a scatter, grouped, and combination
graphs are widely used to look for correlations and meaningful relationships. — Techniques such as curve fitting, tolerance intervals, and three—dimensional rotation
are used more frequently here than in other applications. — Graphs such as surface, contour, probability, and abstract graphs are used more
frequently in these types of applications. — There is no limit as to how much data can be included on graph as long as it is legible. — Greater emphasis is placed on content than appearance. — Color may or may not be used. — Final graphs are generally in the form of hard copy (a paper printout) or on a computer
screen. Monitoring and controlling — Maj or foeus is on observing one or more measurements/values over time (monitoring)
to determine whether actions should be taken (controlling). — Sequence graphs are generally used, particularly time series. — Line and column are the most widely used, point types to a lesser extent. and area
types occasionally. ~ When a reference such as budget, plan, or goal is known it is often included. a When a reference exists, deviation graphs are sometimes used in which only the
difference between the actual and reference are shown. Both period and cumulative
data are sometimes used. _ Greater emphasis is placed on content than appearance.
— Color may or may not be used. — Final graphs are generally either on hard copy (a paper printout) or computer screen. Presentation , — Major focus is on conununicating specific information from one person or group of
people to another person or group of people. a Graphs can contain large amounts of data if they are being presented to a small group
using overhead transparencies or handouts. When presenting to a large audience using
35mm slides, the material on each slide is greatly reduced. — Any type of graph can be used as long as it is appropriate for the audience and legible
to everyone. — Techniques such as the inclusion of pictures, the use of perspective, graduated fills,
etc., are used more frequently in these applications than in the two applications above. — About equal emphasis is placed on content and appearance. — Color is used extensively. — Final graphs are generally in the form of 35mm slides, overhead transparencies, or
video projection. Publications, reports, reference documents, etc. — Applications range from simple bar graphs for newspapers to complex graphs for
technical publications. — The major focus varies with the application. — The types of graphs, enhancements, amount of detail, size, etc., vary depending on the
subject, the audience, or the publication. — About equal emphasis is placed on content and appearance. — Color is used extensively. — Final graphs are generally in the form of hard copy. 167 168 Graph (continued) Methods for improving the value and ease of understanding of graphs Many methods have been developed to increase the amount of information encoded into
graphs and to make them easier to understand. Some of the techniques apply only to
speciﬁc types of graphs; others are applicable to almost ail types. Summarized below,
alphabetically, are representative examples of many of the major methods used today. For
detailed information see the entries referenced with the examples. Additional variable encoded with symbols The size of An additional variable can be encoded in many symbmscii‘ﬁgsai: ways. In this example it is done by varying the sizes 39133233:
of the plotting symbols (circles). Varying color, additional
shading, patterns, shapes, or line thickness, are vanable' other methods. See Symbol. Conﬁdence intervals to show probabilities Methods have been developed for indicating conﬁdence limits and intervals for many types
of graphs. See Conﬁdence Intervals and Range Symbols. 8 1 2
Fmad curve I Conﬁdence D
a interval 1
B
4 e # Confidence
intervals
4
Conﬁdence 2
interval lo; 2
ﬁtted curve
0 U
o 2 4 e e 10 A s c o E A s c
Point graph with ﬁtted curve Column graph Box graph
Direction of changes
:] Favorable
_ Untavorable
Measure A
By means of arrow heads and color coding, the
. . . . Measure 8
direction of change and whether or not It IS favorable
can be encoded. See Change Graph. MeasureC
Measure D Changegrapho 20 40 so so 100 Drop lines used to help locate data points 14
1 2
Thin lines help the viewer's eye 1&0
relate a data point and its value or 6
location. See Drop Line. 2
O A 2 4 6 a B o o 1 2 3 4 5
Line graph Scatter graph 4r—Fills are used to highlight particular data A wide variety of ﬁlls are available to differentiate data series,
highlight differences, or call attention to particular data. See
Fill, Silhouette Graph and Difference Graph. Examples of fill
are also presented in the reviews of most of the major graphs. Focus placed on ranges When ranges or spreads are important, the traditional bars or columns are D
sometimes eliminated and only the 0
ranges plus some inner value such as 3
average or median are shown. See Bar A I. uppervaluas Graph and Column Graph. 0 2 4 6 B ”“510'3852 Class 3 Bar range graph Column range graph Graph (continued) Methods for improving the value and ease of understanding of graphs (continued) Frame shifted for clarity B E .
0.1—— Amount of shill
To avoid having data points appearing on s Q
the axes or scale lines, the frame and scale 4 4 '
lines are sometimes shifted slightly '
horizontally and/or vertically. See Shifted 2 2 3
Frame and Scales. 0 ° I
D 2 4 5 B 10 10
Frame not shifted Frame shined Multiple variables encoded into symbols . Complex symbols.
When several variables are to be such as faces. can encoded, the symbols become more complex. be used to encode
multiple variables. Symbols that are capable of encoding large See Chemo”
numbers of variables are sometimes called Faces icons. See Icon. 0 2 4 6 B 10
Pictures or images used to expedite orientation and improve appearance Pictures, images, or icons are
sometimes used to orient the viewer
and improve the appearance of the graph for presentation purposes. See
Pictorial Graph. Projections of data ”Condition 1 Graphs are often used to project or Condition 2 estimate the future values of a data
series. The projected portions of
the graph are generally clearly differentiated. See Projection. o '
JFMAMJJASOND Time—b Reference lines to make deviations stand out B ,;_, a .— ,
Reference lines can be used to compare actual 6 5 s A
data against or Simply t0 pomt out a value of ja
interest. Drop lines, columns, or bars, might 4‘_§——. 4 a
extend all the way to the zero axis or stop at 2,——. ; 2 0% .
. . . . . if Beterenca :‘_ {Reference
the reference line to htghhght the devrations. ; rune : Inna
' 0 r—t r—r‘ O I —l— r—‘I
See Reference Line. 0 1 2 a 4 5 o 1 2 a 4 5i Drop lines to zero axis Drop lines to reference Scale bars used to indicate equal increments on graphs with different scales \ Wh I 25 _______________ 23 22
en SCH CS RIC ‘ 2° ______________ 22 _______________ _ 21,3
expanded, comparisons 15 2, ________________ 21.5 =1 vertical unit
between graphs can be W
misleading. Scale bars 5 . .  =1 vertical unit I=1 “emca' “mt 21.4
21.2
hBIp reduce [his prOblem' D l I  I  I l 13 I l 1—l—r I 21 l l—l—l_ l SCCSCﬂlCBaTS 012345678910 012345678910 012345678910
Scale bars for visually relating data plotted on graphs with different scales 20 19 Scales expanded for clarity 90
“3° ________________ i This portion 01 as . _ en   ********* the scale on
In order to magmfy that portion 50 m: [graims“ as
of the graph that contains the data 40 been . 34
under study, the scales are m 3:323:21 "“0 32 sometimes expanded. See Scale. 0 “a“! 0" the
A s c o E F 9'39“ at “‘3 no ﬁght ABCDEF 169 170 Graph (continued) Methods for improving the value and ease of understanding of graphs (continued)
Shadows projected onto flat surfaces Shadows projected onto walls Three—dimensional graphs are many times difficult to
visualize. One method for assisting in the visualization
process is to project a shadow or outline of the data onto the
walls of the graph. See ThreeDimensional Graph. ishowing only slices or proﬁles of threedimensional graphs —— Only selected planes are plotted
An additional method for gaining a better understanding of threedimensional data graphics is to display only selected
planes, slices, or profiles. See Slice Graph and Profile Graph. Sketching boundaries to show patterns of upper and lower values . . 10
Lines are sometimes drawn that approximate the major upper and lower
values of a data series to emphasize how
the outer values change and how the spread
changes. See Envelope. Enveiope CN#G>W ismoothing to make data easier to analyze ‘
When data points are spread out or if they have large ﬂuctuations from time period to time
period, it is sometimes helpful to superimpose a line or surface over the data to approximate
the general shape, or slope of the data. Shown below are three examples of such techniques.
See Curve Fitting and Moving Average. Polynomial fitted line
' Fitted surlaoe 3 month moving average o 2 4 a B 10 . JFMAMJJASDNDJFMAMJJASONDJFMAM
Polynomial line ﬁtted to Slurface fitted to three Moving average applied to
scatter graph dimenSIonal scatter data line graph Supplementary grid and scale added  Supplementary scale
Supplementary grid lines To condense two or more graphs into one and make
certain relationships easier to spot, a supplementary grid and scale are sometimes added. See Supplementary
Scale/Grid. isymbol type and placement to improve readability
New symbols have been developed as well as ways of displaying them. The three examples
shown here address the problem of overlapping plotting symbols. See Symbol. data data data data point points DOiI'IlS poinls 0.8 0.9 1.0 1.1 1.2 as 0.9 1.0 1.1 1.2
Sunflower symbol Data points stacked Data points jittered —Symbols used to replace bars or columns Instead of displaying two data series as two sets of bars
or columns, symbols are occasionally used to represent one of the data series. This technique is most widely I
used when one of the data series is to be used as a D _ _
reference. See Bar Graph and Column Graph. E — o I I
0 1 2 3 4 5 B A B C D E Graph (continued) The use of multiple graphs in conjunction with one another Using graphs in conjunction with one another sometimes has a synergistic effect, in that the
value of the multiple graphs is greater than the sum of the value of the individual graphs.
The examples below demonstrate some of the many ways multiple graphs are used
together. They also illustrate some of the advantages of such a technique. Multiple graphs superimposed on one another 10 Data
One of the most widely used methods for a gems A
combining multiple graphs is to superimpose 6 58%:‘33
two or more graphs on top of one another. The 4 Data
resulting graph is sometimes referred to as a genes C
combination graph. See Combination Graph. 2 O '90 '91 '92 '93 '94 '95 '96 '37
Multiple graphs juxtaposed to one another (with complementary data) When two or more graphs are placed immediately .
adjacent to one another they are often referred to ;
as juxtaposed. They may be above and below or _Oneaxis
sidebyside. With complementary data, the 51”“ graph B if graphs are assisting one another to present
broader, more meaningful information to the viewer. Three wellknown examples illustrate the idea.
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An XBar/Fl chart is widely used in the ﬁeld of
quality control. The upper graph displays
sample averages and the bottom graph the
spread of sample values. See Control Charts. Multiple graphs juxtaposed to one a Oneaxis
pom: graph 0 2 4 s 6 1o
Oneaxis graphs are added to the side
and/or top of scatter graphs to show how
data is distributed along an individual axis.
See Mar...
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 Fall '07
 JasonDaida

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