Fundamentals of Engineering Graphing as a Communication Tool GSMST

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? Graphing as a Communication Tool

3 Objectives Introduce basic chart types Basic equation types Good graphing practices Chart examples

4 Which Type of Graph? What kind of data is it? What is the message?

5 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 "1 st Quarter", the year "2004", or "Resistance, Ω") are used for information purposes.

6 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).

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

8 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.

9 Bar Chart THOUSANDS OF UNITS 1st QTR2nd QTR3rd QTR4th QTR QUARTERLY SALES 2001 REGIONAL SALES EAST WEST NORTH X-Axis (abscissa) and label Y-Axis (ordinate) and label Legend

10 Title Data labels Pie Chart

11 Range Bar Graph Figure Range bar graph

12 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

13 Scatter Plot Time (sec) Speed (rpm) ????

Linear and Logarithmic Scaling Linear axis: Logarithmic axis:

15 Three Common Equation Forms Linear Y = mX + B Thermal Expansion Power Y = bX m Wind Force Exponential Y = be mX Population Growth

16 Linear: Thermal Expansion of Pipe Length, L L =  (T – T o ) + L o L =  (  T) + L o (Form : Y = mX + b) TT L LoLo  1 T = Final temperature T o = Initial Temperature  = Coefficient of thermal expansion  L o = Initial length at  temperature T o  T = T - T o

17 Power: Wind Force on Road Sign Wind Force on a Sign (F = P A) P = V 2 Where P = pressure in lb/ft 2 V = velocity in ft/sec (Form Y = bX m )

18 Power Relationship Y = bX m Linear Form: log Y = log b + m log X Y* = m X* + b*

19 Exponential: Population Growth Y = be mX Linear Form: ln Y = ln b + m X Y* = b* + mX

20 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).

21 What could be improved? ABCD Bar Spacing Title Axis labels Color or shade bars

22 Are there still problems? A B CD Units produced by Divisions A – D in July Divisions Units In Thousands

23 Example Hand Graph with Data

24AU 2006 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)

25 Is your message how stable the fatality rate has been… Year Traffic Fatalities In Ohio Number Of Fatalities Note The Poor Choice of Y-Axis Increment

26 …or that fatalities seem cyclical? Note that zero has been suppressed

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

28 Safe Driving in Ohio

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

30AU 2006 Monthly Earnings of College Students Pie Chart

31 Earnings Differences for Men and Women

32 Students earning less than $400 per month?

33 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.