# Rules for Graphs

The following rules for graphs are enforced in physics 1100. Each rule will have some examples showing bad graphs (and what exactly makes them bad) and good graphs. All of the graphs are actual graphs that were submitted by students, with identifying information removed.

### Use graph paper or a computer program such as Excel or Google Sheets

Why? If you draw a graph free-hand, it is difficult to make it accurate.

This graph is hand drawn on lined paper, not graph paper. (Another thing to note is that the percentages of the three data points don’t add to 100%!)

This graph was plotted on a graphing calculator. Note that the graphing calculator does not include any values on the x or y axes, doesn’t label the axes (and because there are no labels there are no units), and doesn’t have a title. If you don’t have a computer on which to make a graph, use a website like Google Sheets to do your graphs.

Good graph example:

This graph was plotted using a computer program. It is much easier to read. (In addition, the percentages of the three data points add up to 100%, as they should!)

### Show each individual data point

Be clear about what each of your data points are. Why? Some graphing software makes a line that goes between data points without actually showing the points. This isn’t scientifically meaningful, and doesn’t allow anybody to see the actual data that was collected in the experiment.

This graph doesn’t show any of the individual data points — it only shows a meaningless line that goes between the points.

Good graph example:

This graph shows all of the individual data points. The line is not necessary to see the trend of the data. It is linear and slopes upward.

### The scale on both axes must be consistent

In other words, the interval between numbers must be the same everywhere along the horizontal axis, and everywhere along the vertical axis. Why? If you change the spacing between numbers, then you can’t make an assessment of whether or not the data is linear.

Note that the x-axis scale is not consistent. The first square has a value of 0.1, then the next two squares have a value of 0.2, then the next square has a value of 0.5, then the next two squares have values of 0.05… Note also the lack of units on both axes, and the fact that connect-the-dots was played.

If you look at the vertical axis of this graph, it starts at -0.100, then decreases to -0.900, then jumps to 0.100 and then increases to 0.700. Remember that negative numbers get smaller when the absolute value of the numbers get bigger! (If you can’t remember, ask yourself how much money is more money: owing somebody \$100 or owing somebody \$900.)

Good graph example:

The spacing on the x-axis is consistent. Each spacing has a value of 0.2 kg.

### Put a title on the graph

A graph should be understood by looking at it, even if the reader is not sure what you are doing. A title allows anybody looking at the graph to understand what they are looking at.

This graph tells nothing about what is being plotted. There is no title, and the axes are not labeled and have no units. This data could be literally anything!

Good graph example:

This graph title tells me a lot more about what experiment was performed.

### Label both axes and include units

The information on a graph should be scientifically meaningful. If it is not clear what is being plotted, then the graph is not meaningful. If units are not included in your graph, then it’s unclear exactly what you are plotting. Remember that units are just as important as the quantities that they describe!

This graph has no label on the vertical axis, but it does have units. It should say: time for one oscillation (seconds). The horizontal axis has a label but no units. It should say: angle (degrees). Note also that the student who made this graph played connect-the-dots with the data.

Good graph example:

This data has been plotted with a title, clearly labeled axes, and units. A nice smooth fit line was used between data points.

### Don’t play connect-the-dots

A scientific graph is used to show a relationship between independent and dependent variables. All of the information on the graph should be meaningful. Drawing lines between each data point, like the child’s game of connect-the-dots, is not scientifically meaningful. It does not allow us to understand the true relationship between the independent and dependent variables.

Note how there is a line drawn between every single data point. That connect-the-dot line does not add any meaningful information to this graph.

Better graph example:

This data does not include a fit line at all. It is better to not include a fit line than to play connect-the-dots, if you are not sure what type of fit line to use. A good example would have included a linear fit line (as the data is linear, it just doesn’t change much with respect to time).

### Use the correct type of fit line

If the data is linear, use a linear fit line. If the data is not linear, use the correct type of fit line. If you draw by hand, just draw a smooth line (don’t connect-the-dots) that follows the trend of of the data. If you are using computer software, it is better not to add a fit line if you don’t know what type to use. Why? The fit line helps us to see through any variations in the data that could be caused by inaccurate lab procedures or calculations. If the wrong type of fit line is used, then it is not scientifically meaningful. In addition, the fit line can be used to interpolate and extrapolate data. The wrong type of fit line will lead to incorrect interpolations and extrapolations.

This graph uses a linear fit on data that is not linear. The data is actually a square root relationship, but it’s fine to just not include a fit line if you’re not sure what kind of relationship it is!

Good graph example:

This graph uses the correct type of fit line for the data. Notice how it doesn’t connect-the-dots, but makes a smooth curve through the data.

### If there are two sets of data, there should be two fit lines

Why? Remember, the point of a fit line is for us to interpret the relationship between independent and dependent variables, and for us to interpolate and extrapolate data. If the fit line is not correct, then it is not going to help us in our pursuit of science. Usually the “one fit line for two sets of data” is an issue with how the graphing software is used. The data needs to be entered into the program as two separate data sets.

This graph shows two sets of data, but only has one fit line.

Good graph example:

This graph has two sets of data, and one fit line for each.

### Do not use Excel’s “line mode”

In Excel, “line mode” will not create the type of graph that we are interested in. It creates a completely meaningless graph. Use “scatter plot” instead.

This graph was created using line mode in Excel. It separates the x-axis data from the y-axis data in a completely nonsensical way. Line mode might work for some things… but not physics graphs! This graph leaves me completely unable to determine what relationship (if any) the angle of swing has with time.

Note also that there are no axes labels or units on this graph, and that the creator of this graph played “connect-the-dots” with the data.

### Use the correct type of graph

The types of graphs used in physics 1100 are scatter plots (to determine if there is correlation between variables) in which there are no fit lines included. A line plot which shows each data point with the correct type of fit line, when we know that there is a relationship between the independent and dependent variables. The third type is a bar graph, when there is a relationship between independent and dependent variables, but when there is a qualitative independent variable that cannot be graphed numerically.

This is a bar graph used to plot quantitative data. A line graph should have been used instead.

A pie chart is not one of the approved types of graphs. This should be a bar graph.

This is the correct type of graph (bar graph) because the independent variable is qualitative. However, the question asked to plot the average percentage over each trial as a function of color. This graph does not show that information. Instead it shows the number of cubes by color plotted as a function of trial number. Just because you are using the correct graph type doesn’t mean you are following the instructions!

I am not sure what kind of graph this is, but it is not a line graph, as it should be for this type of data.

This graph is plotting quantitative data in a bar graph. It should be a line graph.

### Unless otherwise mentioned, use the horizontal axis to plot the independent variable and the vertical axis to plot the dependent variable

Most of the time, we want to understand the relationship between the independent and dependent variables. Therefore we usually plot the IV on the horizontal axis, and see how the vertical axis information (DV) changes. There are going to be a couple of exceptions to this rule. One of which is if we can swap the IV and DV in order to calculate the slope of a graph to get a meaningful quantity such as mass or resistance.

This graph meant to show how the position of an object changes with respect to time. In that case, the independent variable is time and should be on the horizontal axis. Note also the lack of units on each axis, and the connect-the-dots.

Good graph example:

This data shows the independent variable (time) on the horizontal axis, and the dependent variable (position) on the vertical axis.

Your professor is probably older than you are. Please make your graph easy for them to read! Also, it’s generally a good idea to make efficient use of space and make your graph easy to read for anybody, not just your professor.

Note how all of the data is squished into a tiny section of the page. Rather than do this, expand the horizontal axis so that it takes up the entire page. (Note also that this graph does not contain a title, and also plays connect-the-dots.)

Good graph example:

This graph makes efficient use of space in both axes. It is much easier to read without having all of the data squished into a small space.

### Understand the meaning of the spacing used on the vertical axis

Note the spacing between tick marks on the vertical axis. If the spacing is very small, then there may not be a dramatic relationship between the IV and the DV. It is good practice to start the vertical axis at 0, and then let your computer software do automatic scaling on the vertical axis. If you are drawing by hand, ask yourself what a good spacing would be. Why? It is not correct to say that there are large changes in the DV when there is actually a very small change compared to the average value.

This graph isn’t technically wrong or bad, but the spacing on the vertical axis is just 0.2 seconds, which is about 10% of the average value. This makes the data appear to have a rather large upward slope.

Good graph example:

This is the same data shown with the vertical axis scaled from 0. Note how it is a lot more clear now that the dependent variable essentially does not change with respect to the independent variable.

### Don’t just include (0,0) as a data point

Don’t just include (0,0) in your data unless it was a data point that you collected.

This data includes (0,0) for all sets of data. It makes the data appear to be linear. Notice that it doesn’t necessarily “look wrong”, but it is wrong. It would imply that it took zero seconds for an object to move a space of about a meter!

Good graph example:

This data does not include (0,0) as data points, because they are not data points! It’s also more clear from this data that the relationship between independent and dependent variables is not linear.

### Plot all data from a single trial on a single graph

Unless your professor asks you to place two sets of data on one graph, each experiment that you conduct should have its own graph. It’s especially important not to put one set of data on two graphs… then it becomes impossible to meaningfully compare any trends throughout the entire duration of the experiment.

This data all comes from a single experiment, but is placed on two separate graphs with differently scaled axes. This means that we cannot look at this data and determine what trend (if any) there is between position and time. Note also that the y-axis, which has negative values, is positioned above the x-axis instead of going below the x-axis, which is where negative values belong.

### Pay attention to your data and ask yourself if it makes sense

It’s always a good idea to do a “smell test” on your data. Does it look like it makes sense? Does the shape of the data appear consistent with what you expect? Sometimes just looking at a graph can help you to see if you made an error somewhere in your calculations or measurements. If you’re not sure, ask your professor for help or clarification.