You can think of the six points labeled x1 through x6 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.
- 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?