Physics 211

Error Analysis

Computer Intensive Physics

IMAGE imgs/Error_analysis_repeated_01.gif


Consider the situation when we measure an experimental quantity (call it x)
n times. In general, every measurement may yield a different value of x because
conditions of measurement are not precisely identical for the different
measurements. It is clear that if one takes the average value for these n
measurements, the effect of random errors will be decreased.


Let the average of these measurements be denoted by xave, and let xibe a
particular measurement, the ithmeasurement. Then

IMAGE imgs/Error_analysis_repeated_02.gif

For example, suppose four determinations of g yield 9.80 m/s2, 9.79 m/s2, 9.82 m/s2,
and 9.83 m/s2. Then

IMAGE imgs/Error_analysis_repeated_03.gif

We therefore write our result as g = 9.810 [!]0.009 m/sec2.


This discussion has been taken mostly from the lab manual for Physics 106 at
the University of Illinois. Reference from Laboratory Manual for Physics 222,
Reynolds and Joseph, 1987.