If it is not alr

eady there, move the black bar at the bottom of the graph up so that it crosses the Y axis at 1. The bar should go right through the red circle. Notice the numerical indicator of the black bar immediately to its right.

The deviation of the red circle from the bar is 0, so you won't see a red rectangle on the right-hand portion of the graph. The line between the bar and the blue circle is the deviation of the circle from the bar. It has a length of 1. Notice that the height of the blue rectangle is 1. The area of the blue rectangle is also 1.

The green line has a length of 2 and the height of the green rectangle is 2 and its area is 2² = 4. The total height of the rectangles is the sum of all the line lengths: 0 + 1 + 2 + 3 + 4 = 10. This height is the sum of the absolute deviations from the bar. It is marked below the rectangles. The sum of all the areas of the rectangles is 30.

Your goal is to find the placement of the bar that gives you the smallest total area. This will be the value that minimizes the sum of the areas of the rectangles. Move the bar up and down until you think you have found this value. Then, to make sure you are correct, click on the "OK" button at the bottom of the graph. This will move the black bar to the correct location. If nothing changes, you found the correct location on your own.

Now, change the value of the green circle from 3 to somewhere between 2 and 3. You move the circle by clicking on it and dragging it. Notice that the value of the point is shown in green.

Next, find the value that minimizes the sum of squared deviations for the new data.

Now move the blue circle to somewhere between 3 and 4 and again find the value that minimizes the sum of squared differences.

See if you can find a rule to determine which value will minimize the sum of squared deviations?