Measurement I


Precision of measurements with respect to measurement size.
Topics: Measurement theory, precision, standard deviation. Pre-requisite skills: Basic understanding of standard deviation. Approximate completion time: Under an hour.
*Provide sufficient detail to verify that the assignment was completed in a meaningful manner.*
Applet by Wolfgang Christian
The above applet shows a red dot which will serve as the origin (that is, the point where we define x and y to be 0). We can create circles of arbitrary radius by double-clicking at any point in the applet window. 1. Using the mouse, double-click at a point such as to create the largest circle that will fit inside the applet window. (a) Using the mouse, display the x and y coordinates of a point that lies on this circle. From these coordinates, calculate the radius of this circle. (b) Repeat step (a) nine more times for various locations around the circle. Therefore, you should have a total of ten radius calculations for this circle. 2. Now use the mouse to create a circle that has roughly half the radius of the first. Using the mouse, calculate the radius of this circle ten times as in the previous step. 3. Calculate the standard deviation for both calculations. Which is larger? 4. It is often said that larger measurements are more precise. Explain how your results correlate with this statement. 5. Which group of measurements would likely be more precise -- measuring the diameter of a golf ball or the diameter of a basketball? Explain. (Assume you use the same measuring instrument in both cases.)
Helpful Resources Standard Deviation by Marcus Kazmierczak (includes calculator utility). Standard Deviation Demonstration by Richard Hall (includes calculator utility). Standard Deviation Tutorial by David Dice (includes calculator utility) Statistics Every Writer Should Know - Standard Deviation by Robert Niles. Example of Standard Deviation by George Woodbury
Return to Web Assignments