The Joint Committee for Guides in Metrology (JCGM) has compiled a comprehensive guide to the expression of uncertainty in measurements . A shorter guide by Bell  is available from the National Physical Laboratory in the UK. Both are accessible free of charge on the internet.
ANSWERS FOR EXERCISES
11.1 Potential background variables in the planetarium setup are landmarks such as people or the camera stand. To isolate the effect of the Milky Way other stars in the sky must be removed. You should make sure that there are no sources of polarized light in the planetarium. Note that the diagram does not contain all potential background variables. What would for instance happen if the arena was not level?
11.2 Left for the reader.
The variation of the length is greater than that of the diameter. Putting the values into Equation 11.7
, however, we see that the diameter term of the variance is almost a factor of two greater than the length term. To decrease the total variation we should therefore aim to decrease the standard deviation of the diameter.
11.4 Two of the three observations from 14 to 16 are beyond two standard deviations. The eight points following observation 16 show a trend.
1. Montgomery, M.C. (1991) Introduction to Statistical Quality Control, 2nd edn, John Wiley & Sons, Inc., New York.
2. BIPM, IEC, IFCC, ILAC, ISO, IUPAC, IUPAP and OIML. (2008) Evaluation of Measurement Data – Guide to the Expression of Uncertainty in Measurement ...