Analysis 1

Mean and Variance

The measurements you make in the lab are subject to error. We can formalize this idea by thinking of a measurement of<math>x</math>. This may be the number of counts per minute from the ML or the RS labs, or it might be a reading of the Hall voltage, etc etc. Nature determines the expectation value of the measurement. We'll use the mean as the expectation value (instead of, say, the median):

<math>\mu = \langle x></math\rangle.

If you take a lot of data, such that you have <math>N</math> measurements of <math>x</math> -- <math>x_i</math>, then the sample mean is given by

<math>m = \frac{1}{N} \sum^N_i x_i </math>

which should be familiar. In order to estimate the error on

<math>\sigma = \langle (x-\mu)^2 \rangle