ARE GPS MEASUREMENTS ACCURATE OR PRECISE?

Concepts

• There is a difference between accuracy and precision
• Measurements can be both precise and accurate
• Repetition of experiments can increase both precision and accuracy
• Error is present in all measurements
• Outside conditions can effect results

Materials

• 20 marbles
• Holding cup
• Curved tube
• Meter stick
• Scale
• 2 pieces of carbon paper
• 4 pieces of graphing paper
• Pencil and paper
• Partner

Required skills

• Knowledge of basic math
• Knowledge of units

Background

Throughout the last few sections you have learned that GPS is a precise-positioning tool that has the ability to record position with millimeter accuracy. But what is precision and accuracy? How and why do they differ? And what determines if the data you are collecting is accurate or precise?

Accuracy is a measure of how close the result of the experiment is to the true value. Therefore, it is a measure of the correctness of the result. Precision is a measure of how well the result has been determined, without reference to its agreement with the true value. It is a measure of the reproducibility of the result. Precision and accuracy are important to scientists because they help to determine if data is useable or not. With GPS, scientists look at position data from different sites to see if it is close to the predicted value (accurate) and if the data values are the same from day to day (precise.) What they have found is that the more time they spend taking data at one location the more accurate the position measurements become. After 1 hour, measurements may vary 10 mm, while after 1 day, they vary 3 mm and after 7 days, they only vary by 1mm. When the data isn't accurate or precise, scientists know that something is either wrong at the site or interfering with the satellite signals before they reach the antenna.   

Interference can be caused by anything-- a car driving by, other radio signals in the area, and even the atmosphere itself. Because there is no way to predict what is effecting the results of an experiment, all data values must contain some uncertainty, or error. Uncertainty , or error, for a group of values is an estimate of the differences in values from trial to trial. These errors are divided into two groups, systematic and random, depending on their origin. Systemmatic errors , errors in accuracy, make results differ from their "true" value , but are reproducible. These usually are a result of operator error. For example, a person could be reading a ruler that is marked in millimeters, but recording values in centimeters. While all of the values would have the same units, they would be different from the true value which would be in millimeters. Random errors , errors in precision, effect the reproducibility of results from test to test. These are usually a result of errors that occur in the instrument itself (a broken thermometer, rough edges inside a slide) and the experiment surroundings ( the experiment is done in water instead of air, the experiment table is moving during a test.)

Helpful Formulas

• Average

Procedure

Part I:

Determine which of these is accurate, precise, both or neither:

 _______  ________  _______  _______

Part II:

1. Set up the tube.

2. Measure the height of the tube from the table top to the starting point. Also measure the length of the tube, and the distance from the bottom of the tube to the floor directly below it. Record all measurements on paper.

3. Weigh all 20 marbles separately. Add the weights together and divide the total weight by 20 to get an average weight for each marble.

4. Release a marble from the start of the tube and have your partner record where it lands on the floor. Measure the distance from the floor under the end of the tube to the spot where the marble landed.

5. Make a sandwich of two sheets of graph paper and two sheets of carbon paper (the graph paper up and the carbon (shiny) sides down.) Tape the carbon paper sandwich over the area on the floor where the marble landed. It is important that the paper does not move during the experiment. A mark should appear every time a marble lands on the paper. Label each piece of graph paper with a trial number.

6. Release 10 marbles down the tube, one marble at a time. Try to release the marbles the same way each time. The marbles should be landing in the same general area on the graph paper. If the marbles do not land on the paper start over and move the paper to the area where the marbles do land. Have your partner collect the marbles after each trial and place them in the cup.

7. Replace the graph paper between the two pieces of carbon paper and repeat with all 20 marbles.

8. Repeat steps 4 and 7, with new graph paper, this time changing the force on the marble each time you release one.