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Plotting Points Sample Problems


Try these sample problems on first your own so you can see if you understand. If you need help or just want to check your answers, you can reveal the answers.
You can download graph paper here (Acrobat (PDF) 7kB Sep10 08).

If you need to print the steps for reference, download the worksheet with plotting points steps (Acrobat (PDF) 35kB Sep10 08). You can also download the questions (Acrobat (PDF) 31kB Jul24 09) to print them.

The Problems

Problem 1. You collect samples from several of the islands and seamounts on the Hawaiian-Emperor chain, and determine their age. Plot the distance from Kilauea for each sample against the age of the sample.
Volcano Name Age (Myr) Distance (km)
Kilauea 0 0
East Maui 0.75 182
Kauai 5.10 519
Necker 10.30 1058
Laysan 19.90 1818

1. Make sure that you have two variables to work with (two columns of data).
In this case, you have two columns of data, age and distance, so you don't need to do anything else for step 1.

2. Decide which of the variable is going to be represented on the x-axis and which will be on the y-axis.
In this case, the problem does not clearly say which axis should be age and which should be distance. We will go ahead and assume the first column of data (age) will be on the horizontal X-axis.

3. Label the axes on your plot and determine the appropriate scale (if the graph is not already labeled).
Since a graph is not already provided, we will need to do this. Get out a piece of graph paper and draw axes and label them.

Next, we need to determine our appropriate scale. Since the age data goes from 0 to 19.90 Myr, it makes sense to have the x-axis go from 0 to 20. Halfway between 0 and 20 mark 10 and, if you want, mark 5 and 15 halfway between 0 and 10 and 10 and 20, respectively.
For the y-axis, distance goes from 0 to 1818. It will be pretty easy to plot if we have the y-axis go from 0 to 2000 and mark 1000, 500, and 1500 miles respectively.
Plotting Points Sample Problem 1.1


4. Begin by plotting the first two pairs of numbers (the top row of numbers).

The first pair of numbers is 0,0, so this will be at the origin.
Plotting Points Sample Problem 1.2


5. Continue to plot pairs of points from the table (in rows) until you have plotted all the points.

For East Maui, you will need to approximate where 0.75 Myr is on your x-axis and where 182 is on your y-axis. since these are both less than a tenth of the way to the last label on the axis, they should be very close to the origin. Proceed with the rest of the points, making sure that Kauai is close to a quarter of the way along the x- and y- axes.
Plotting Points Sample Problem 1.3

6. Check to make sure your final graph has the same number of points as pairs of data in your table.

This may seem silly, but it is a common mistake to make to skip a set of numbers, especially with larger data sets. So make sure you have 5 data points on your graph. You might want to label them to make sure.

Problem 2. You want to create a topographic profile of elevations across the Fox River Valley in Appleton. A profile is essentially a graph of elevation versus distance. Graph the following information. In this example the distance is the distance from the intersection of S. Mason and S. Spencer and the elevation is feet above sea-level.
Distance (mi) Elevation (ft)
0 800
0.1 795
0.2 790
0.3 795
0.4 790
0.5 765
0.6 735
0.7 735
0.8 785
0.9 790

1. Make sure that you have two variables to work with (two columns of data).

In this case, you have two columns of data, distance and elevation, so you don't need to do anything else for step 1.

2. Decide which of the variable is going to be represented on the x-axis and which will be on the y-axis.

In this case, since distance is horizontal distance over the ground, it makes sense to make that the x-axis. This also agrees with the general rule that the first column of data should be plotted on the x-axis unless otherwise instructed.
Plotting Points Sample Problem 2.1

3. Label the axes on your plot and determine the appropriate scale (if the graph is not already labeled).

Since the distance data goes from 0 to 0.9 miles, it makes sense to have the x-axis go from 0 to 1.0 miles. Also, notice that the data is regular, with distances in icrements of 0.1. If we make sure the axis goes 10 squares long (or a multiple of 10), and it goes from 0 to 1.0 and plotting will be easier. Mark 0.5 half-way along the x-axis.
The y-axis is a little bit trickier, since the data only goes from 733 to 791. If we make the origin 0 ft., all the data will be scrunched up. So it makes sense to have the y axis go from 700 ft to 800 ft, since that is a smaller range and encompasses all the data. Mark 750 ft halfway between 700 and 800 ft. If you make the y-axis 10 squares, then each square will be 10 feet, which will make plotting easier.
Plotting Points Sample Problem 2.2

4. Begin by plotting the first two pairs of numbers (the top row of numbers).

From 0 mi on the x-axis go up to 800 ft on the y-axis. Put a point.
Plotting Points Sample Problem 2.2

5. Continue to plot pairs of points from the table (in rows) until you have plotted all the points.
Continue to plot the points. The first 5 should be near the top of the graph, since they are all very close to 800 ft.
Plotting Points Sample Problem 2.4

6. Check to make sure your final graph should have the same number of points as pairs of data in your table.

You should have 10 data points on your graph. If you don't, go back and find the one you missed!

Problem 3. Records from Mercer Creek near Seattle show a 12-year flood (a flood with a recurrence interval of 12 years) has a discharge of 812 ft3/sec , a 6-year flood has a discharge of 670 ft3/sec, a 3-year flood has a discharge of 612 ft3/sec, and a 2 year flood has a discharge of 504 ft3/sec. Plot this data with recurrence interval on the x-axis and discharge on the y-axis.
1. Make sure that you have two variables to work with (two columns of data).

In this case, the data is in the text, so go ahead and make a data table.
Discharge (ft3/sec) Recurrence interval (years)
812 12
670 6
612 3
504 2

2. Decide which of the variable is going to be represented on the x-axis and which will be on the y-axis.
In this case, the directions explicitly say to put the recurrence interval on the x-axis, so even though it is in the second column of the data table above, we will put it on the horizontal axis.

3. Label the axes on your plot and determine the appropriate scale (if the graph is not already labeled).
The recurrance interval goes from 2 to 12, so there are several good options for your x-axis. It could go from 0 to 15 or 2 to 12, or even 0 to 12. Whichever span you choose, be smart about it and make it so that a whole number of squares equals 1 year - it will be much easier to plot the points. Mark an intermediate point or two On the Y axis, the data go from 504 to 812, so a good range might be 500 to 1000. Mark 750 half-way.
Plotting Points Sample Problem 3.1

4. Begin by plotting the first two pairs of numbers (the top row of numbers).
In this example, we first plot 12, 812, which should be in the upper right hand region of your graph.
Plotting Points Sample Problem 3.2

5. Continue to plot pairs of points from the table (in rows) until you have plotted all the points.
Plot the rest of the points as accurately as you can. The other three points will be in the lower left-hand area of the graph.
Plotting Points Sample Problem 3.3

6. Check to make sure your final graph should have the same number of points as pairs of data in your table.
You should have 4 points on your graph. If you don't, figure out which one you missed.

Next Steps


Think you understand? Then go to wamap.org to take the online quiz.

If you still need help, you can go back to the explanation page or look at some of the links below.

Need more practice?


HotMath has some problems where you can practice plotting pairs of data.

The Oswego (NY) City School District has a fun little game with Billy Bug to practice plotting data on an x-y plot.



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