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Unformatted text preview: Graphical Communication
Charts and Graphs Unit Objectives Present various graphing options Describe the utility of each option Provide examples of each option Develop transformations that allows nonlinear data to be linearized Document the principles associated with good graphing practices
2 1 Types of Chart I Pie Charts Bar Graph (Histogram)
– LeafandStem Scatter Plots – Error Bars – BoxandWhisker – Scatter Matrix 3 Types of Chart II MultiVariable Plots – Surface Plots – Contour Plots – LocationandBubble Radar Plots Vector Field Representation 4 2 Pie Chart Used to compare elements within one category The complete circle represents the total and the sectors represent the fraction of a specific element The fraction can be expressed as an absolute and/or relative (%) value Some sectors can be extracted for emphasis
5 Pie Chart Example
5 TJ, 2% 45 TJ, 22% 85 TJ, 42% 70 TJ, 34% Gas Coal Oil Trash
6 3 Bar Graph (Histogram) Used to illustrate categorical or discrete data Discrete Frequency Distributions
– Shows the number of items associated with a specific category Comparison Graphs – Used to compare items within a category in absolute or relative terms
7 Bar Graph Example Present the following data as a frequency distribution: 40, 41, 41, 42, 42, 43, 43, 43, 43, 44, 44, 46, 46, 48, 49
5 4 Frequency 3 2 1 0 40 41 42 43 44 45 46 Stress (MPa) 47 48 49
8 4 Negative/Positive Comparisons
50 440 STS97 200 380 PR008 150 520 H223a 50 450 GR844 100 350 Drag Lift GR8T4 200 400 AP334 300 200 100 0 100 200 300 400 500 600
9 Force (N) Relative Comparison
Aluminum Brass Bronze Cast Iron Magnesium Steel Titanium 0 5 10 15 20
6 o 25 Linear Expansion (10 / C) Airfoil Type
30
10 5 Absolute Comparisons
300 Air
250 Auto Train PeopleMiles (Million)) 200 150 100 50 0 1940's '50's '60's '70's '80's '90's
11 Fractional Comparisons
250 Wave Tidal Wind Hydro 200
Power Generation (TW) 150 100 50 0 France Spain Italy Austria Norway
12 6 StemandLeaf Similar to a horizontal Bar Graph The value of all elements associated with each are also shown, however, and constitute the bar Cumulative and median information is often added to the chart More descriptive than Bar Graph More “busy” than a bar chart
13 StemandLeaf Example Present the following data in a stemandleaf format: 13, 14, 15, 15, 19, 20, 25, 28, 28, 28, 33, 33, 33, 36, 37, 39, 41, 42, 47, 48, 54, 59, 62 Cumulative number of elements Number of elements in the “leaf” containing the median leaf” 5 10 (6) 20 22 23 1 2 3 4 5 6 34559 05888 333679 1278 49 2
14 7 Scatter Plot Used to graph experimental data Data represented as markers on a two axis chart in a number of ways
– Individual data points – A mean with error bars – Boxandwhisker representations Multiple variable can be handled as combination plots or a matrix of plots Trend lines can also be included
15 Scatter Plot Examples
5 4 3 2 1 0 0 0.1 0.2 0.3 0.4 0.5 5 All Data Points 4 3 2 1 0 0 0.1 BoxandWhisker 0.2 0.3 0.4 0.5 5 4 3 2 1 0 0 0.1 0.2 0.3 0.4 0.5 5 Mean and Error Bars 4 3 2 1 0 0 Data and Trend Line 0.1 0.2 0.3 0.4 0.5 16 8 BoxandWhisker I
A chart where the median, and first and third quartiles are represented as a box with a line through it The min and max values are then represented as a bar at the end of a line extending out from the box These lines cannot be longer than 1.5 times the interquartile range (i.e. Q3Q1) from the box
17 BoxandWhisker II Point beyond this bars are outliers, and are represented as circles Box width is often the sample size Finally, the mean is shown as a star This type of display contains a large amount of information 18 9 BoxandWhisker Example Draw the boxandwhisker plot for the following data
Temp. = 20 oC Stress = 40, 41, 41, 42, 42, 43, 43, 43, 43, 44, 44, 46, 46, 48, 49 MPa Temp. = 80 oC Stress = 61, 62, 64, 64, 66, 66, 66, 66, 66, 66, 67, 67, 67, 68 69 MPa
Stress
80 70 60 17 16 50 40 30
N= 15 15 20 80 Temperature 19 Combination Plots Used to compare the data sets associated with two dependent variables using a common abscissa Two ordinate axes are therefore required
– One on the left and one on the right Good for illustrating the tradeoff associated with changing a specific factor
20 10 Combination Plot Example
Engine Performance Curves
700 600 500 70 60 50 40 30 20 Power Output (kW) Efficiency (%) 10 0
0 2 4 6 8 10 400 300 200 100 0 Engine Speed (1000 rpm)
21 Scatter Matrix An array of multiple scatter plots Used to show all comparisons between different specified variables Used primarily in statistical studies Allows possible relationships, and their strength to be identified The array contains both comparisons of all variable combinations (i.e. xy and yx)
22 Efficiency (%) Power (kW) 11 Scatter Matrix Example 23 MultiVariable Plot Used to show how a dependent variable changes with respect to two independent variables (factors) Result is a surface existing in a three dimensional space (axis system) Can also be shown using multiple curves on a two dimensional graph Also, a 2D graph can be used if the dependent value is represented as a color/contour or the radius of a circle
24 12 Surface Plot Example
1 0.8 0.6 Dependant Value 0.4 0.2 0 0.2 0.4 0.6 0.8 1 0 1 2 3 4 0 5
25 4.2 2.8 1.4 Y Value X Value Contour Plot Example
4.8 4.4 Dependant Value
0.81 0.60.8 0.40.6 0.20.4 00.2 0.20 0.40.2 0.60.4 0.80.6 10.8 4 3.6 3.2 2.8 2.4 Y Value 2 1.6 1.2 0.8 0.4 0 0.4 0.8 1.2 1.6 2 2.4 2.8 3.2 3.6 4 4.4 4.8 0
26 X Value 13 Two Dimensional Plot
1.2 1 0.8 0.6 0.4 Z Value 0.2 0 0.2 0.4 0.6 0.8 1 1.2 0 0.5 1 y = 0.5 y = 1.0 y = 1.5 y = 2.0 y = 2.5 1.5 2 2.5 X Value 3 3.5 4 4.5 5 27 LocationandBubble Example
42.5 42 41 40.5 40 39.5 76 75 74 73 72 71
28 Longitude (degrees) Latitude (degrees) 41.5 14 Radar Plot Used to illustrate how the value of a dependent variable varies with direction or time The dependent value is distance from the center of the chart The independent value is the angle from the (up) vertical Points or arrows can be used and/or a continuous lines can be drawn
29 Radar Plot Example
Average Wind Speed
N 60 50 NW 40 30 20 10 W 0 E NE SW SE S 30 15 Vector Field Representation Shows how a vector dependent variable varies with position Represented as an arrow where the arrow tail is at the location, and the arrow length and orientation is the vector magnitude and direction Can be two or three dimensional Colors/contours can also be superimposed onto the vector field
31 Vector Field Example 32 32 16 Linear Transformations I Straight lines are easier to use and visualize, therefore, it is often useful to transform nonlinear data such that the result is a straight line The independent and dependent values are transformed using a specific expression and the result is then plotted on regular linear axes Alternatively, the data can be plotted on a log on semilog graph
33 Linear Transformations II
y bx a
Plot y against x slope = b, intercept = a Plot log y against log x slope = a, intercept = log b Plot log y against x slope = a.log e, intercept = log b a. Plot log (1/(1y)) against x (1/(1slope = a.log e a.
34 y bx a y be ax y 1 e ax 17 Linear Transformations III
x y bx a
b ya x
Plot 1/y against 1/x slope = a, intercept = b Plot y against 1/x slope = b, intercept = a y b x a Plot y against x1/2 slope = b, intercept = a Plot (yy1)/(xx1) against x slope = c, intercept = b+cx1
35 y cx 2 bx a Chart Formatting I
Have the origin (0,0) on most plots Use only as many sigfigs as needed for axes In bar charts have rankable labels increasing to the right In the landscape mode the xaxis (abscissa) should be on the right Plot experimental data using markers Use large enough fonts and markers 36 18 Chart Formatting II Use different markers and line types for different data sets Have no more than four data sets plotted on one graph Do not fit curves through every data point for many fluctuating points Add a trend line if necessary Plot predicted data using curves Keep background visuals to minimum
37 Diagrams and Pictures Figures have to be numbered, and possess a descriptive title Figures have to be referred to in the text Diagrams and pictures should be appropriately annotated Figures should not be too “busy” 38 19 Summary Graphs are the primary element by which data is communicated A number of options exist that allows data to be represented Nonlinear data can be linearized by using a specific transformation Care should be taken to format a graph or diagram appropriately
39 20 ...
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This note was uploaded on 11/08/2010 for the course MECH 438 taught by Professor Johnl during the Fall '10 term at Manhattan College.
 Fall '10
 JohnL

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