Fundamentals of Engineering Graphing as a Communication Tool GSMST
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?
Objectives • Introduce basic chart types • Basic equation types • Good graphing practices • Chart examples
Which Type of Graph? • What kind of data is it? • What is the message?
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, Ω") are used for information purposes.
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).
Example of Categorical Data Character Character Label Label Numeric Each row of this table may be considered a category with two labels.
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.
2001 REGIONAL SALES 90 80 70 60 EAST 50 THOUSANDS OF UNITS 40 WEST 30 NORTH 20 10 0 1st QTR 2nd QTR 3rd QTR 4th QTR QUARTERLY SALES Legend Y-Axis (ordinate) and label X-Axis (abscissa) and label Bar Chart
Pie Chart Title Data labels
Figure 4.47 - Range bar graph Range Bar Graph
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
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
-20 -15 -10 -5 0 5 10 15 20 0.1 1 10 100 Linear and Logarithmic Scaling Linear axis: Logarithmic axis:
Three Common Equation Forms • Linear • Y = mX + B • Thermal Expansion • Power • Y = bXm • Wind Force • Exponential • Y = bemX • Population Growth
Length, L a L 1 Lo dT 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
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)
Power Relationship Linear Form: log Y = log b + m log XY* = m X* + b* Y = bXm
Exponential: Population Growth Linear Form: ln Y = ln b + m XY* = b* + mX Y = bemX
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).
What could be improved? • Bar Spacing • Title • Axis labels • Color or shade • bars 12 10 8 6 4 0 A B C D
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
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) AU 2006
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
…or that fatalities seem cyclical? Note that zero has been suppressed
…or? • Maybe you really wanted to graph traffic fatalities per 100 million miles driven to show how safe it is to drive in Ohio.
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? College Students with Jobs
MonthlyEarnings of College Students Pie Chart AU 2006
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.