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## Fundamentals of Engineering

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**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.