We have all heard the phrase “A picture is worth a thousand words” before. When we are presented with unfamiliar, large or otherwise cumbersome data it can be beneficial to construct a graph – a diagram – of the data to help us visualize patterns and trends in numbers. By making a picture of the data we are able to use our visual senses to help our analytical mind interpret data. Making graphs by hand is also a good kinesthetic exercise, allowing us to become more familiar with the information that we have collected.
Why do we make graphs?
When we collect data the easiest way for us to collect it is to use a data table, columns are for the kind of data we are recording, rows are for each individual observation. For example, I watched the cars going by my house one morning, I counted the number of cars that went by every ten minutes and built the following table.
If I look at this table closely, I can see that early (7:00 – 7:20 AM) there is almost no traffic and as I get closer to 9:00 (when many people start work) traffic gets very heavy, but once work has started traffic tends to slow down. This is a small table and we can see the patterns fairly clearly. What if this was a much larger table, what if the numbers were not as easy to understand, they might be very big or very small. Perhaps the relationship between them is not so clear as in this example. By constructing a diagram that visually represents the relationship between the variables, the time and the number of cars in our example, we can gain a better understanding of our data.
What do we use to draw a graph?
Typically we use special paper, graph paper, that has a grid of lines that are usually regularly spaced at right angles to each other to draw graphs by hand. The spacing of the lines is not as important as our ability to define an appropriate scale for our graph. We also want to use a rule or other straight edge when we draw lines on our graph paper, not just for neatness but because our measurements later on will be made from the lines that we draw.
Graphing Terminology
It is important to learn some terms when working with graphs. Here is a sample graph plotting the following data. (In this example it is not important where the data came from or what it means, it is just being used to help us describe the graph format.)
A graph is defined by two (or more) axes. The xaxis or more correctly abscissa is the axis where we plot our independent variable, the variable that we choose and control. The yaxis or ordinate is the axis on which we plot our dependent variable (the one that DEPENDS on our independent variable). The point where the two axes cross is called the origin of the graph.
The scale is probably the most important part of the graph next to our data. The scale determines what values we have assigned to the grid lines on the paper. In this case I used four grid lines for every unit of value on both axes. This means that every line has a value of 0.25. With some practice you should be able to estimate between your finest markings on your scale down to about 2/10ths of the division or in this case about 0.03 units. In this example that is about 1% of the full scale of this graph! This is part of what makes a graph such a powerful tool, not only can it help us visualize data, but we can accurately read values from a properly constructed graph. When making your first few graphs it may take several tries to get the scale quite right.
Mark a data point on your graph with a thin but easy to distinguish mark. Use your scale and count over first on the abscissa then up (or down) on the ordinate. To help you keep track of where you should put the point use your straight edge to mark the abscissa and then move along it to the correct place on the ordinate. Some people like to make simple dots when making their graphs, I think that they can be too easily confused as errant pen marks. The coordinates are the values (X and Y) from our table. We often will not include these on a graph but were included here in illustration.
Graphing our Example Data
Here is an example of a graph constructed from our sample data. When I chose the scale for this graph I chose to make each grid line on the abscissa worth five minutes and each grid line on the ordinate to be worth one car. I used red to mark the values because it is a contrasting color. My data is well spaced and uses the full page, making my graph easy to read. (Click on the graph above for a larger image.)
Wrapping Up
Graphs are an important way to represent scientific data. They allow students to both visually and kinesthetically interact with the data they have collected. Soon we will discuss using your computer to make graphs. In case you have trouble finding graph paper (ask in your local office supply store) here is a link to an image of graph paper you can print at http://www.printfree.com .
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