Statistics

Dynamic geometry has proven itself as a very valuable medium for visualizing statistical concepts such as the mechanism behind a least squares regression line or the meaning of the correlation coefficient. The plotting capabilities, dynamic loci, and dynamic transformation with calculated quantities available Version 3 of Sketchpad makes construction of these statistics sketches easier and more powerful.

The sketches on this page are available individually (below) or can be downloaded as a package.

The Centroid of 6 Points
The coordinates of a point (xMean, yMean) are computed as the mean of the x-coordinates and mean of the y-coordinates of six points. As the given points are dragged, the effect on the centroid can be observed.

Questions: How many points can you get to be down and to the left of the centroid? How far to the right does the centroid move if you drag one point to the right one centimeter? How far does it move if you drag two points two centimeters? Does the centroid move when you drag the origin of the coordinate system? How about if you change the unit of the coordinate system?

Version 3 makes it easy to compute the coordinates of the centroid and to display the formulas that do so.

The Normal Curve
In this sketch you can vary the parameters that define a normal curve. As you change the parameters, the curve changes dynamically. You can display two limits of integration and the area under the curve between those two limits. The area is computed by numerical integration. A button moves the curve into standard form.

As you drag the unit point on the x-axis, the entire curve scales accordingly. This is accomplished through a subtle trick which you can experience as follows:

  1. In a blank sketch create axes.
  2. Place a point on the x-axis. Notice that as you drag the unit-point, this "free" point does not scale accordingly.
  3. Draw a line (not a segment) from the origin to the unit point.
  4. Hide the axes and place a point on the line.
  5. Show the axes and drag the unit point. Notice that, because the point is defined relative to a line rather than relative to the axes, its position scales.
Chi Square in Perspective
In this sketch we have Sketchpad as a data entry vehicle for six numbers in a 2 x 3 table. You drag six points to change the numbers. The question is, do the men and women in the sample have significantly different hair colors? You can show totals, expected values, and the computation of the chi-square statistics

We really didn't expect to come up with a visualization of this idea. Let Bill Finzer know if you find it useful.

Return to the Foyer.

Sketches, scripts, and web pages by Bill Finzer and Nick Jackiw.