 
Summary: Additional notes for PHYS2020
Michael AshleyJune 2004
1 Numerical integration
1.1 Midpoint method
Please see the lecture notes.
1.2 4th order RungeKutta
Please see the lecture notes.
2 Statistical analysis of data
2.1 Moments of distributions
Consider a number of independent measurements of a physical quantity x. Let the
individual estimates be x0, . . . , xn1. Then, we can define various moments of the
distribution. For example:
2.1.1 The zeroeth moment
The zeroeth moment is simply n, the number of samples.
2.1.2 The first momentmean
The first moment is the mean, and can be calculated as follows:
¯x =
1
n
n1
