Fundamentals of Engineering

1
Fundamentals of Engineering

• Graphing as a Communication Tool
• GSMST

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Graphing as a Communication Tool

• It's been said that a picture is worth
• a thousand words
• but when displaying data, what kind of picture
  (graph, chart) should you use? How do you make
  your graph best show what you want?

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Objectives

• Introduce basic chart types
• Basic equation types
• Good graphing practices
• Chart examples

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Which Type of Graph?

• What kind of data is it?
• What is the message?

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Types of Data

• Data values can be numeric or character
  (including numbers and symbols).
• Numeric data (such as 2.3 or 12) are used in
  positioning features on the graph in a way
  proportional to their numeric value.
• Character data (such as "1st Quarter", the year
  "2004", or "Resistance, O") are used for
  information purposes.

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Data can be Organized by Categories

• Categories are groupings of data with something
  in common.
• Categories are described by one or more character
  labels.
• Numeric data for categories are related to the
  entries in each category (e.g. number of
  occurrences, average, sum, percent, or cumulative
  percent).

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Example of Categorical Data
Character Character Label
Label Numeric
Each row of this table may be considered a
category with two labels.
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Types of Graphs

• Bar charts (many forms), pie charts, histograms,
  and line plots are several of the many ways to
  present categorical data.
• Categories are represented on these graphs
  independent of any value their label may have as
  a number.

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Bar Chart
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Pie Chart
Title
Data labels
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Range Bar Graph
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Types of Graphs

• Scatter Plots and Contour Plots are used when all
  variables are continuous
• Scatter Plots are ideal for experimental data
• Scatter Plots place every point based on the
  values of each variable

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Scatter Plot
Time (sec) Speed (rpm) 1 1210 2 1866
3 2301 4 2564 5 2742
6 2881 7 2879 8 2915 9 ????
10 3010
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Linear and Logarithmic Scaling
Linear axis
Logarithmic axis
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Three Common Equation Forms

• Linear
• Y mX B
• Thermal Expansion
• Power
• Y bXm
• Wind Force
• Exponential
• Y bemX
• Population Growth

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Linear Thermal Expansion of Pipe
L a (T To) Lo L a (dT) Lo (Form Y
mX b)

• T Final temperature
• To Initial Temperature
• Coefficient of thermal
• expansion
• Lo Initial length at
• temperature To
• dT T - To

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Power Wind Force on Road Sign

• Wind Force on a Sign (F P A)
• P 0.0036 V2
• Where
• P pressure in lb/ft2
• V velocity in ft/sec
• (Form Y bXm)

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Power Relationship
Linear Form log Y log b m log XY m
X b
Y bXm
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Exponential Population Growth
Linear Form ln Y ln b m X Y b mX
Y bemX
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Good Graphing Practices

• Every graph must have a title and axis labels.
• When more than one data set is shown on the same
  graph, a legend is needed.
• Leave margins at the edges of the paper.
• Graphs must be neat and easily readable (e.g.
  size of graph, large enough font, no text on top
  of data or axes).
• Each graph must include the author and date (on
  the same page with the graph).

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What could be improved?

• Bar Spacing
• Title
• Axis labels
• Color or shade
• bars

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10
8
6
4
0
A
B
C
D
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Are there still problems?
Units produced by Divisions A D in July
10
8
Units In Thousands
6
4
2
0
A
B
C
D
Divisions
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Example Hand Graph with Data
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What is your message?

• The overriding objective in making graphs, just
  like all forms of Engineering communication is
  CLARITY
• Consider the number of traffic fatalities per
  year in Ohio (Courtesy NHTSA)

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Is your message how stable the fatality rate has
been
Traffic Fatalities In Ohio
Number Of Fatalities
Year
Note The Poor Choice of Y-Axis Increment
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or that fatalities seem cyclical?
Note that zero has been suppressed
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or?

• Maybe you really wanted to graph traffic
  fatalities per 100 million miles driven to show
  how safe it is to drive in Ohio.

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Safe Driving in Ohio
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College Students with Jobs

• 270 college students were surveyed to find
  whether they had part-time jobs and how much they
  earned.
• How can we present this data graphically?

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Pie Chart
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Earnings Differences for Men and Women
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Students earning less than 400 per month?
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Hint

• If you're graphing data to answer a question,
  think about which style of graph and which scales
  will best show you the answer.