Technical Writing (AEEE299) LECTURER: Dr. Alexis Polycarpou HOURS/WEEK: 2 TEACHING AREA: Classroom EMAIL: eng.pa@fit.ac.cy

LECTURE Plotting Graphs

Why use Graphs? Suppose we investigate the behavior of a power supply and measure the output voltage as a function of the current drawn from the power supply Iout (mA) 20 40 60 80 100 120 140 Vout (V) 9.9 8.6 8.4 7.9 7.7 7.4 7.1 6.5 Someone asks the question: “What output voltage would be obtained if the current drawn is 37 mA?” 3

We could interpolate numerically, but a graph would allow us to make a reasonable estimate a lot faster

Another question: “How does the output vary with current?” We can try to see this form the numbers in the table, but a graph will immediately show the relationship: Answer: “With the exception of the end points there is a reasonable linear relationship between output voltage and output current.” Hence, a graph is a useful visual aid for displaying results and allows numerical derivations to be made easily.

Anatomy of a graph There are many different types of plots, not all of which are used in technical presentations. The most common employs a symbol to plot each data value on an x-y coordinate plane.

Types of graphs

Bar graphs A bar graph is composed of discrete bars that represent different categories of data. The length or height of the bar is equal to the quantity within that category of data. Bar graphs are best used to compare values across categories. They can be used to show how something changes over time or to compare different times.

Advantages: They can represent data expressed as actual numbers, percentages and frequencies. They are very easy to read They summarize a large data set in visual form They clarify trends better than do tables or arrays They make it easy to compare trends of different quantities

Disadvantages: They require additional explanation They can be easily manipulated to give false impressions They can be inadequate to describe the attribute, behavior or condition of interest They fail to reveal key assumptions, causes, effects, or patterns

Pie charts A pie chart is a circular chart which is divided into slices. The area of each slice is proportional to the quantity it represents. Pie charts are the preferred method for graphing percentages.

Advantages: They display relative proportions of multiple classes of data They show areas proportional to the number of data points in each category They summarize a large data set in visual form They can be visually simpler than other types of graphs They are easily understood from people with no engineering background

Disadvantages: They cannot provide exact numerical data It is difficult to predict trends. They reveal very little about central tendency or behavior It is difficult to compare different sections of a given pie chart, or to compare data across different pie charts They can be easily manipulated to yield false impressions

Line graphs Line graphs, are the most common type of graphs used for the presentation of analytical data. A line graph displays the relationship between two types of information. The information is a series of data points that each represents an individual measurement or data. The series of points are then connected with a line to show a visual trend in data over a period of time.

Advantages: It is easy to determine how a variable changes over time. They can show trends in the data, and make predictions about data that is not recorded They are visually simpler than bar graphs or histograms They summarize a large amount of data in visual form They become more smooth as data more points are added They require minimal explanation

Disadvantages: They reveal little about statistics. They require a small range of data When comparing different set of data they must be of the same quantity and range. They are less suitable when comparing multiple sets of data

Rules for Line Graphs

Rules for Plotting Graphs Title: Every graph should have a title, which should contain a brief description of what is being investigated. Axes: The axes should have clearly marked scales and must be labeled in terms of the quantity (i.e. Output Voltage) and the units (i.e. Volts) in which it is measured.

3) Determine the dependant and independent variables: The x-axis of a graph is always the independent variable and the y-axis is the dependent variable. In most experiments we change one quantity (the independent variable) and observe the effect on the other ( the dependant variable). The x-axis should always show the independent variable (the variable you are changing). The y-axis should always plot the dependent variable (the variable you are measuring) For example, when looking at the effect of temperature on the resistance of a material, you change the temperature and measure the resistance. As such, temperature goes on your x-axis (it is independent) and resistance goes on the y-axis (it is dependent)

4) Scales: They should be chosen so that the points are spread over as much of the graph as possible. Show the numerical values of your scales clearly at frequent intervals. Choose simple scale divisions so that sub-divisions are easily estimated. 5) Points: Plot points clearly as crosses ( + or x) or as circles with centre point or diamonds ♦. Do not use dots. At least six points are required when they lie close to a straight line or smooth curve. More are required in more complex graphs.

6) Multiple Graphs: Sometimes two or three sets of data (though rarely more) are plotted within the same set of axes. You must distinguish between them by using different symbols (X, O ,■,▼ etc) or lines (…………., ________, -----------, etc). Avoid using color for materials, which are going to be printed. It is a bad practice to plot graphs of measurements of two different quantities together using double scaled axes. Its is a good practice to plot the two sets of measurements of the same quantity on the same axis; allows comparison. However they must have the same scale, not one in V and the other in mV.

7) Best Curve: Draw the best curve through a set of points 7) Best Curve: Draw the best curve through a set of points. Do not join individual points by straight lines. Do not draw freehand. If it is not obvious if the best curve should be a straight line or a polynomial curve, check with theory.

8) When taking readings, during the experiments, spread them evenly over a range of values. 9) Drafting the graph: Plot a rough copy of the graph while you do the experiment to ensure that you have enough points.

Describing plots and graphs The main reason that we use plots of data is to describe the data. Data can be described qualitatively using specific terminology: Often we use words that describe the curve or line made by the data: e.g., linear, exponential, asymptotic, periodic, etc. The strength of those relationships can also be characterized using words like strong, moderate or weak Sometimes we use words like increasing and decreasing or positive and negative to describe the relationship of a set of data.

For example: The data on the plot below have a moderately strong negative linear relationship.

Reading data from graphs Plots of data (and simple relationships between variables) can help engineers to understand and predict the behaviour of a device/component or its properties. Plotting known data can help us to visualize the behavior of systems in situations that have not been measured.

QUESTIONS???