Scatter Plot

What is Scatter Plot?

This applet allows the user to input a series of (x,y) ordered pairs and plot them either as a connected function or unconnected data points. Parameters such as minimum and maximum x value, minimum and maximum y value, and x- and y-scale can be set by the user or determined by the applet.

The coordinate plane system was developed by a sick mathematician. As Rene Descarte lay in bed sick, he saw a fly buzzing around on the ceiling. His ceiling was made of square tiles. As he watched, he realized that he could describe the position of the fly by the ceiling tile it was on. After this experience, he developed the Cartesian coordinate system in the 17th century to help visualize functions via plotting function values as ordered pairs. In this system a grid of evenly spaced horizontal and vertical lines is drawn, a center or "origin" is chosen, and horizontal and vertical scales are chosen. Here's an example:

Notice that the horizontal and vertical scales are different, but each one considered alone is evenly spaced. Also, the blue point is labeled with its Cartesian coordinates , the horizontal and vertical movement from the origin, in that order. This is the mathematical convention for naming points.

Another name for the horizontal movement value is the abscissa, and the vertical movement is the ordinate. These terms are more rare now than they used to be, but you might still hear them being used.

Related Resources

• Activity Graph Sketcher
• Activity Graphit
• Activity Multiple Linear Regression
• Activity Regression
• Activity Simple Maze Game
• Activity Simple Plot
• Discussion about From Graphs to Function Machines and Back
• Discussion about Gathering Information from Graphs
• Discussion about Introduction to the Coordinate Plane and Coordinates
• Worksheet Scatter Plot Exploration Questions
• Worksheet Scatter Plot Exploration Questions (doc)
• Worksheet Scatter Plot Record Sheet(Large)
• Worksheet Scatter Plot Record Sheet(small)

How Do I Use This Activity?

This applet allows the user to input a series of (x, y) ordered pairs and plot them. Parameters such as minimum and maximum value, minimum and maximum y value, and x- and y-scale can be set by the user or determined by the applet.

Controls and Output

• The area at the top of the screen is where the plot is displayed.
• The text field labeled Data is where you input the points you want to graph. The points should be in the form (x, y). The parentheses are optional, the x and the y can be separated by a tab or a space and there must be a carriage return between each coordinate pair.
• You can plot up to ten sets of points. To do this, separate each set of points by the word newgraph on a line by itself. You may also specify the color of your graphs by using the following keywords in place of new graph: redgraph, bluegraph, greengraph, purplegraph, crimsongraph, magentagraph, orangegraph, blackgraph, cyangraph, graygraph, and yellowgraph. If you specify newgraph each time, the colors will iterate through the order listed.
• After you input the coordinates, you must press the Plot/Update button to graph them.
• If you have trouble copying data from the applet and pasting it into an Excel spreadsheet, please see our Excel Copy/Paste Help.
• Note that if the Auto Scale box is checked, Scatter Plot will choose appropriate x- and y-axis values for you to view all data on the graph. If you uncheck that box, you can override Scatter Plot's values with your own. This is explained below in the Set Window note.
• You can choose from two plot types. "Connected" draws a line from one point to the next. (Note that before the line is drawn the points are sorted by their x coordinates.) "Scatter Plot" just draws the points as dots on the graph.
• There are three radio buttons which control the gridlines on the graph. You can chose no grid, light grid lines, or dark grid lines by selecting the appropriate radio button.
• Click the Set Window button to change how the graph will appear on your screen. A new browser window should open after you push the button and inside that new window you will be able to adjust values. X min and X max are the minimum and maximum x-values displayed on the graph. Similarly, Y min and Y max are the minimum and maximum y-values displayed on the graph. The X scale is the distance between vertical gridlines if Show Grid is checked. The Y scale is the distance between horizontal gridlines if Show Grid is unchecked. Any changes you make to the window parameters will take effect the next time you click the Plot/Update button. When you are finished, push the Set button followed by the Close button to set the changes and to leave the window. Also note that while the Choose Scale Automatically box is checked, X and Y scale text boxes are uneditable.
• The applet also can tell you the location of any click. Just click the mouse anywhere on the graph that you want to know the coordinates of and the coordinates will appear in the Mouse Position field.
• By entering text into the Title= field you can change the title of your graph. After changing the title hit plot to see the new title at the top of your graph.
• By entering text into the Horizontal Axis = field you can change the title of your x axis.
• By entering text into the Vertical Axis = field you can change the title of your y axis.
• Zoom/Pan buttons. In the upper right corner of the graph, there are three buttons with pictures of magnifying glasses. From top to bottom these buttons represent zoom in, zoom out, and pan, respectively.
  • To zoom in, click the top button to depress, then click and drag over the area of the graph for which you wish to zoom to. The images below show the preimage as the user drags over the area in which to zoom and the resulting zoomed image. Note that after clicking and dragging over the selected area, the zoom in button is automatically released.
  • To zoom out, simply click the middle button. The graph will automatically zoom out by doubling the min and max values of the axes.
  • To use the pan feature, click the bottom magnifying glass button to depress it. Click and drag over the graph and the graph will pan around according to the movement of the mouse. Upon releasing the mouse, the pan button is released.

Description

This applet allows the user to input a series of (x,y) ordered pairs and plot them either as a connected function or unconnected data points. Parameters such as minimum and maximum x value, minimum and maximum y value, and x- and y-scale can be set by the user or determined by the applet. This activity would work well in groups of two to four for about forty-five minutes if you use the exploration questions and twenty minutes otherwise.

Place in Mathematics Curriculum

This activity can be used to:

• illustrate the Cartesian coordinate system
• practice students' pattern recognition skills
• practice students' graph reading skills
• illustrate the relationship between graphical and algebraic representations of functions

Be Prepared to

• answer the question "How can I tell if the data has a relationship?"
• discuss the concepts of positive relationships, negative relationships, data collection, etc.

Related Resources

• Activity Graph Sketcher
• Activity Graphit
• Activity Multiple Linear Regression
• Activity Regression
• Activity Simple Maze Game
• Activity Simple Plot
• Discussion about From Graphs to Function Machines and Back
• Discussion about Gathering Information from Graphs
• Discussion about Introduction to the Coordinate Plane and Coordinates
• Lesson on Cartesian Coordinate System
• Lesson on Graphs and Functions
• Lesson on Univariate and Bivariate Data
• Worksheet Scatter Plot Exploration Questions
• Worksheet Scatter Plot Exploration Questions (doc)
• Worksheet Scatter Plot Record Sheet(Large)
• Worksheet Scatter Plot Record Sheet(small)