Math You Need > Graphing > Plotting Points

Points on x-y plots
can also be called:

Ordered pairs
(Cartesian) coordinates

How do I plot points on a graph?
Plotting geologic data in x-y space

Why should I plot points?

Atmospheric Carbon Dioxide levels measured in the atmosphere above Mauna Loa, Hawaii (modified from Keeling and Whorf, 2003).

In the geosciences, we deal with large volumes of data, both observational and measured. This may be in the form of climate data, rock chemistry, elevation measurements, seismic data, etc. We generally compile data into tables and when we want to know the relationship of one variable to another, one of the easiest ways to do that is to put that data on a plot. Take the table of data to the right. Just looking at it (you can click on the image to open a bigger version in a new window), can you tell what the general trend in CO2 values has been for the past 50 years? Has the trend changed in the past 10 years? How about the last 5 years of record? Does the data vary from month to month? Are there seasonal cycles? So many questions! And they can all be answered with a simple x-y plot.

Monthly Mauna Loa CO2 data (table above) from January 2000-December 2006 plotted on a x-y graph showing trends and patterns.

Bivariate (x-y) graphs help us to visualize and categorize large volumes of data without having to sort through cumbersome data tables. Imagine having to look at the Mauna Loa table as pairs of data (each month for 48 years makes 576 pairs of data!) and trying to figure out the relationship of one variable to another! Or, even worse, a table that isn't organized by date or in numerical order...It's much easier to see on a graph that CO2 has generally increased over the 7 years shown here. You can also see distinct seasonal changes where carbon dioxide is high in May and low in October when the data is plotted on a graph! The rate of change seems to be pretty constant over the time period shown here.

Where is graphing used in the geosciences?

Geoscientists use graphs to illustrate all kinds of issues in the science. In introductory geoscience courses, you may be asked to plot data in conjunction with units that deal with:

  • groundwater
  • geologic hazards
  • glacial advance or retreat
  • climate and climate change
  • deserts and dune migration
  • geologic time and radioactive decay
  • earthquakes and seismic data
  • plate tectonics

If you are struggling to remember how to plot points, this page is for you! Below you will find some simple steps for plotting points on an x-y graph and links to pages to help you with the next steps.

Simple rules for plotting points

Any plot or graph that has two axes is an x-y (or bivariate) plot. One axis (generally, the horizontal one) is the "x-axis" and the other (the vertical one) is considered the "y-axis". But, you can use any variable for either one, all you need is a data set that has two sets of related data. Below there is an example of a set of data points for how basalt melting temperatures change deeper in the Earth.

basalt melting data Table showing how melting temperature of basalt changes with depth in the Earth. Modified from Tarbuck et al., 2008, Applications and Investigations in Earth Science, 6th edition,.

When we plot data on a graph, there are several steps that you can follow to make sure that you don't forget anything:

  1. Make sure that you have two variables to work with (two columns of data). In the case of the table above, the two variables are depth (km) and basalt melting temperature (°C).
  2. Decide which of the variable is going to be represented on the x-axis and which will be on the y-axis. In some cases, you will be provided with a graph that has the axes labeled.
    blank graph paper (melting basalt)
    You can download and print a copy of this blank sheet of paper (click here). (Acrobat (PDF) 105kB Aug13 08)
    A general rule of thumb (and one that many spreadsheet and graphing programs use) is that numbers in the first column of a table will on the x-axis. However, geologists do not always follow this rule, so make sure you check.
    Reversed axes
  3. Label the axes on your plot and determine the appropriate scale (if the graph is not already labeled).
  4. Begin by plotting the first two pairs of numbers (the top row of numbers).
    In the case of the basalt melting temperatures, the first two numbers are (0, 1100). In other words, we are going to plot a point at x=0, y=1100. How do we decide where to put a point? Follow these simple steps:
    1. First, find the value for x on the x-axis. In the case of basalt melting temperatures, x = 0; so, find 0 on the x axis.
      finding x=0
    2. Next, find the y-value - in this case, y=1100, so find 1100 on the y-axis.
      step 2 for plotting (0,1100)
    3. Your point should be plotted at the intersection of x=0 and y=1100. (If you draw one line up vertically up from x=0 and another line horizontally from y=1100, where they cross is where you should put your point!
      step 3 for plotting (0,1100)
    4. Finally, plot the point on your graph at the appropriate spot.
      step 4 for plotting (0,1100)
  5. Continue to plot pairs of points from the table (in rows) until you have plotted all the points.
    The second set of points: x= 25, y= 1160:
    melting basalt 25

    The third set of points: x = 50, y = 1250:
    melting basalt 50 km

    The fourth set of points: x = 100, y = 1400:
    melting basalt 100 km

    The last set of points: x = 150, y = 1600:
    melting basalt 150 km
  6. Your final graph should have the same number of points as pairs of data in your table.
    melting basalt final plot

You can download and print a sheet with the steps on it here (Acrobat (PDF) 35kB Sep10 08).

Some practice problems

When you are comfortable with the steps shown above, you can move on to the plotting points sample problems, which have worked answers.

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