A SMALL DOSE OF STATISTICS
Dr. Don Stierman - updated 2006  

“A man with one watch knows what time it is.  A man with two watches is never quite certain.”[1]  

            We have a similar problem with geographical coordinates supplied by a GPS receiver.  As you stood in one location, latitude, longitude and elevation kept changing.  No, plate tectonics was not responsible for this apparent motion.  One problem associated with measurements is uncertainty, or error.  By “error” I do not mean mistakes or incorrectness.  “Error” in this context refers to the degree of uncertainty.

             For example, a friend with a simple GPS receiver informs you where her seat in the Glass Bowl is located in terms of latitude and longitude.  If you set your GPS unit to navigate to that location, how close will you get?  Inside the stadium?  In the correct section?  Within ten seats or rows?  Within two seats or rows?  Can you identify her seat by means of latitude and longitude alone, or does GPS technology lack that degree of accuracy?  The difference between the true location and your GPS location is the error.  

            During the field GPS lab, students used Trimble GeoExplorer II GPS receivers to collect location information.  These locations were stored in GEII memory, downloaded to computers, and differential corrections calculated.[2]  You have lists, provided by the teaching assistant, of corrected and uncorrected locations.  Instead of latitude and longitude, these locations are listed in terms of “military grid”, or UTM (Universal Transverse Mercator), a Cartesian (X and Y axes at right angles to one another) system many find more convenient for local maps than latitude and longitude.  What is the best value you can write for each location where GPS readings were collected?

Kinds of errors

Introductory probability

The Normal Distribution