Module Identifier PX34010
Module Title DATA HANDLING AND STATISTICS
Co-ordinator Professor Geraint Vaughan
Semester Semester 1
Pre-Requisite Core Physics Modules at Level 1
Course delivery Lecture   8 lectures (first half of semester)
Practical   36 Hours Laboratory. 12 laboratory sessions (3 hours each)
Assessment
Assessment TypeAssessment Length/DetailsProportion
Semester Exam1 Hours End of semester examination  20%
Semester Assessment Course Work: Young's Modulus experiment  30%
Semester Assessment Course Work: Photometry Experiment  30%
Semester Assessment Course Work: MathCad exercises  10%
Semester Assessment Course Work: Theory Exercises  10%

#### Learning outcomes

After taking this module students should be able to:
• explain the nature of random error in experimental data
• use the Gaussian distribution and appreciate why it applies in so many cases
• calculate the mean and standard deviation of data following a simple, unbiased Gaussian
• recognise the effect of inter-dependence of measurements and extreme values on data sets
• combine several different errors to derive a final error
• identify the most important source of error in an experiment and concentrate on reducing that error
• fit a straight line to experimental data and evaluate the standard error in the slopeand intercept.
• write a simple MathCad program to model a physical system.

#### Brief description

This module is a laboratory-based course where the handling of data in selected experiments is treated in parallel with a course on the theory of measurement, the nature of experimental errors, random and systematic. The course provides an introduction to the basic statistics encountered in Physics, including the Binomial, Poisson and Normal distributions, and simple least-squares regression. The estimate of standard error, the combination of errors and the optimum design of experiments to reduce the final error in the most efficient way are covered. Applications of these concepts will be made through practical work and computational work using MathCad.

#### Content

Use of MathCad for statistical problems

Theory of measurement

Random and systematic errors
Accuracy and Precision
Mean and standard deviation
Gaussian, Poisson and Binomial distributions
Combining uncertainties
The Least Square Principle, graphing data and fitting a straight line to data

Experiments:

1. Photometry experiment. Determine the temperature of an incandescent filament by optical measurements.

2. Young's Modulus experiment - Determination of Young's Modulus, with special care taken to estimate the random uncertainty in the final result. Identification of the parameter contributing most to the final error.

#### Transferable skills

Use or STOMP CAL package