# Mean

#### Description

You can download a pdf file that contains a complete worksheet for using this sketch with students. (In order to view a PDF file, you will need to download Adobe Reader.)

You can think of the six points labeled *x*_{1} through *x*_{6} as representing six data values such as six heights, six incomes, or six cholesterol levels. Try dragging the points. Notice that you cannot change their *y*-coordinates. We are only interested in their *x*-coordinates.

The vertical dashed line is movable. You use it to look for a good place to define as the "center" of the six points.

Two tools for finding a "center" are shown.

- Press the
*Show Differences*button to show the differences between the points and the line and the algebraic sum of these distances. Drag the dotted line and notice how these values change. - Hide the differences and show the squares. Drag the dotted line and notice how these values change.

#### Questions

- Describe at least two ways to get the sum of differences to be negative.
- What can you do to get the sum of differences to be zero?
- If you change the positions of the data points, is it always possible to adjust the dashed line so that the sum of differences is zero? Why or why not?
- Write a definition for the center of data values that uses the sum of differences.
- Under what circumstances will the sum of squares be zero?
- If you change the positions of the data points, is there always a position of the dashed line that makes the sum of squares zero? Why or why not?
- How can you use the sum of squares to define a center?