Questions and Problems on Statistics

1. What is an accurate measurement?
    
2. What is a precise measurement?
    
3. Describe a measurement that is accurate, but it is imprecise.
    
4. Describe a measurement that is precise, but inaccurate.
    
5. Using simple optics it is shown that the relationship: dsinθ = mλ describes the angular position of diffracted light of wavelength λ, when it is "blocked" by an obstacle of width d. Use a strand of hair, a laser and an ordinary ruler to determine the wavelength of light. (Either estimate the hair's thickness, or measure it using a raveling microscope.)
    
6. On what basis can you judge an experiment to have produced good results?
    
7. What is the currently held estimate for the age of the universe?
    
8. How long after the Big Bang did the basic elements start to form? How much later did basic atoms begin to form?
    
9. How does a GPS determines location? What are the roles of the satellite in this working? How many are used?
    
10. What are random occurrences? What is a (probability) distribution?
     
11. Give examples of three different types of probability distributions and compare them.
     
12. Write down the expression for a Gaussian distribution and describe each variable in that expression.
     
13. Use a Spreadsheet to create the graph of a Uniform distribution from 10,000 random events.
     
14. Same as in the above, but now create a Normal distribution for 1,000 random events.
     
15. Use the procedure described at the NIST's site to calculate the uncertainty in value of the area for the data table of Ws and Ls in the Statistics Page.