General aims:

• 1. To explain how the variations observed in the measurement of a physical quantity can be represented by a frequency distribution.

• 2. To be able to determine the mean, standard deviation and standard error from a data set.

• 3. To understand and apply straight line fitting using least squares and weighted least squares techniques.

• 4. To be familiar with the Gaussian, binomial and Poisson distributions and to know how they relate to each other.

Objectives: On completion of the course the student should be able to:

• 1. Construct a frequency distribution from measurements of a physical quantity.

• 2. Define the mean and standard deviation for a distribution.

• 3. State the standard error in the mean and know how it relates to the standard deviation.

• 4. Explain the difference between random and systematic errors

• 5. Define the Gaussian distribution.

• 6. List important properties of the Gaussian distribution.

• 7. Explain the application of Gaussian distributions in the treatment of random errors.

• 8. Combine errors in functions of several variables.

• 9. Describe the principle of least squares fitting (simple and weighted).

• 10. Apply this principle to fitting a straight line.

• 11. Determine the values for the gradient and intercept of a straight line fit.

• 12. Define the Binomial distribution.

• 13. State the mean and standard deviation of the Binomial distribution.

• 14. Define the Poisson distribution.

• 15. State the mean and standard deviation of the Poisson distribution.

• 16. Explain how the binomial, Poisson and Gaussian distributions relate.

• 17. Do a wide range of examples based on the above material.