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# Essential Graph Elements

In this section, I want to show you the essential graph elements and the information that every graph should contain.  In later sections, we will discuss the details on how to insert these elements in Excel.

# The minimum acceptable graph

Let’s take a look at the graph of free fall data below.  The data was taken by dropping a small cylinder through a tube that had photogates located every 15 centimeters along its length.  The data from the photogates was processed to produce a plot of position vs. time.  The cylinder is dropped manually after the data collection software is started, so the initial point does not occur at time t = 0 s.

At the bare minimum, every graph should have the following…

### Title

The title should be descriptive of the data set.  You may have been taught to put in the generic title “y-axis vs. x-axis”, so you would be tempted to label this graph as “Position vs. Time”.  I would argue that this information is already shown as the axis labels.  Showing what is unique about the data set should be the aim of your title.  In the experiment this data was taken from, we adjusted the angle of the tube that had the series of photo gates.  The titles of the graphs could then have the angle in the title.

### Data Points

Without your data points, you wouldn’t have a graph, so this might seem obvious.  However, it is important that your data points be large enough to be seen, or small enough to be seen separately.  This tells your audience at least two important things:

1. How many measurements you made.

### Axis Labels

You must tell your audience what the axes represent.  Give each a clear title and include the units.  Make sure that the labels are large enough to be readable, especially if you are going to present the graph in a talk at in a large lecture hall.

# Beyond the minimum

In most situations, you are not just reporting your data, you are trying to extract additional information from it.  To do this, you will want to add more information to the graph.  You can also add a few elements to make the graph easier to read.

Notice the differences between the two graphs shown.

### Trendlines

Trendlines are mathematical fits that provide a model to your data.   They are not simply lines connecting the data points.  You should avoid adding lines to your data points, except in a few rare cases.

Excel has several different models built into the program, including linear, logarithmic, power, and polynomial.  Often one of these describes the physical situation of your data.

Excel also has the option of a “Moving Average”.  You should avoid this fit in almost all situations.  Trained scientists assume that the lines on a graph are the result of some mathematical model.  The moving average is mathematically determined, but it is really only used to trace out a smooth curve to the data.  If you don’t have a mathematical model, it would be a better idea to just leave the data points unconnected.  Later, I’ll describe the process of adding trendlines.

### Equation and R-squared Value

Excel can plot the equation of your trend line if you check the appropriate boxes in the “format trendline” option box.  Unfortunately, Excel will always show this equation using x and y as variables.  The program also will almost always show too many significant digits in this equation.  Thankfully, you can click on the equation and edit it appropriately.  I did so in this situation, so that now the equation is shown in terms of position y and time t.

The R-squared value is a measure of the quality of the fit to your data.  A value of 1 suggests that the data follows the model almost exactly.  A value of zero suggests that the data is almost completely random, and the model doesn’t fit well at all.  There is a bit more subtlety to this, but this description is enough to get us started.

### Legend

If you only have one set of data, the legend is not absolutely necessary, but if you have more than one set of data on the chart, it is imperative that it be included.  I almost always include the trend line in the legend.  It is a good idea to format each set of data using differently shaped symbols.  Each fit should be displayed differently as well.  Using differently dashed lines helps your audience to tell clearly the difference between the trend lines for each data set.

### Grid lines

The grid lines on a graph can help your audience compare values at different locations a little more easily.  However, in some situations the grid lines might be distracting.  Excel gives you the option of adding major gridlines and minor gridlines.  You can even decide on the spacing between each type of grid line.

I very rarely add the minor grid lines, as the graph tends to become too busy when these are present.  A good rule of thumb would be to only add a maximum of ten grid lines in either the x or y dimension.  If you are going to make a picture of your graph and scale it, you should be very careful of grid lines.  In particular, if you make a digital image of a large graph, but then make it smaller, the scaling algorithms can often remove random grid lines, making your graph look awkward.

# Review:  Essential Graph Elements

The essential graph elements that should be included in almost every graph are…

• An informative title
• Clearly visible data points.
• Appropriate labels on each axis that include units.
• A trend line showing the mathematical model of the fit of your data, when appropriate.
• A legend if more than one type of information is included.
• Grid lines when appropriate.

You are now ready to do one of the following:

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