An Example of Imperfect Data taking:

Students with stop watches timing a ball drop.

An example of Pefect data taking:

Perfect Stop Watches

But, we don't live in the perfect world of measurements. All measurements have errors. This is unavoidable. This means that All measurements are approximate.

Measurments often depend upon the precision of the instrument that you use to make the measurment. No instruments have infinite precision.

On an exam:

• Your ability in applying the material learned in this course
• Errors associated with how the exam was graded. These errors come in two forms; one is much worse than the other:

  1. Random error (can be corrected for - see below)
  2. Systematic Error (extremely serious if you don't know it exists)

  These Errors works like the following:

  

  What we measure is X but what we are interested in is the distribution of the true variable, T. To measure T, however, we have to know what the random error, e_r and systematic error e_s is.

  Without knowledge of e_r and e_s , T can never be accurately measured. This potentially is a huge problem.

  What is e_r

  

  Random errors increase the dispersion or the variability of the data around the mean value. These errors are associated with apparatus or method used in obtaining the data. All data sampling is subject to random error, period. The individual stop watch measurements made by each student is a source of random error in the mean time. There is no way to avoid it.

  

  What is e_s ?

  

  Note: the above graphic contains an error. It should say systematic error does affect the average instead of random error (which does not affect the average).

  Systematic errors mean that different methods of measurement are being applied to the same variable. This means that the position of the mean is strongly effect. For example, suppose there are two patrolment on the freeway both with identical radar guns. Except that one of them systematically reads 5 mph higher than the other due to a "calibration" error back at the station. Which policeman do you want to speed by?