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Average Value of a Hand-Drawn Function

Daniel Gries (Hopkins School)

Draw your own function by clicking on the screen and dragging the mouse to set y-coordinates of points to be smoothly connected. This applet will interactively show you the average value of your function from point a to point b, which are draggable points in the applet. This rather simple interface can be helpful in discussing the concept of an average value. The applet also illustrates through the use of optional shading the visual definition of average value as the height of a rectangle with area matching the area under the cuve for positive functions.

For example, the function shown in the screenshot below has f(1) = 0 and f(5) = 2, and the average value (shown as the y-coordinate of the horizontal blue line segment) appears to be 1, halfway between the y-coordiantes at a and b.  By adjusting the curve, it is simple to show that this is not always the case.

This applet requires the free Flash Player 9 browser plug-in available from Adobe.

Average Value Applet

Open the Average Value applet in a separate window

Daniel Gries (Hopkins School), "Average Value of a Hand-Drawn Function," Convergence (February 2010), DOI:10.4169/loci002639