Introduction to Probability and Statistics
MODULE CODE
CREDIT VALUE
DELIVERY
Module Aims
Aim 1
To give students a grounding in basic concepts and techniques for applied statistics.
Aim 2
Establishing the underlying concepts and probability theory behind statistical techniques.
Aim 3
Introducing students to aspects of inferential statistics and how these can be applied to answer statistical questions.
Aim 4
Developing the practical skill of students enabling them to tackle statistical problems with real world data.
Module Content
The module will include the following topics.
Core Concepts: Measures of central tendency and dispersion; Data presentation.
Data and Surveys: Sampling; Questionnaires; Bias, error and precision.
Probability: Experiments and outcomes; Assigning probability; Axioms and interpretations; Addition and multiplication laws; Conditional probability.
Probability Distributions: Random variables; Probability density functions; Cumulative distribution functions; Binomial, Poisson, and Normal distributions.
Statistical Inference: The central limit theorem; Significance testing and confidence intervals; z-tests; t-tests; two-sample t-tests; 𝜒𝜒2-tests; Non- parametric tests – sign tests, Mann-Witney tests and Wilcoxon tests.
Statistical Packages: The use of R in analysing data will run in parallel with the taught material. The emphasis is on how statistical software can be used to tackle statistical problems aligned with the syllabus.
There will be a strong emphasis throughout the module on understanding the context of the practical use of statistics.
Learning Outcomes
On successful completion of this module, a student will be able to:
Teaching Methods
The module will be delivered on campus, with weekly lecture and tutorial sessions.
Printed notes will be provided in advance for each section of the course to support and enhance students’ preparation and engagement during class sessions. Lectures will follow the notes, with discussions of the main theoretical topics, and study of examples of the applications of the theory. There will be a strong emphasis on student involvement in discussions in lectures, to encourage a more active approach to learning the material, and to allow the delivery to be tailored to build on the students’ current understanding.
R will be used to demonstrate real-life applications, helping students better understand and assimilate key statistical concepts. This approach enhances engagement, fosters critical thinking, and strengthens data analysis skills.
Regular formative work in tutorial sessions will allow students to internalise the mathematical ideas and methods developed in the lectures, and lead to the development of problem-solving skills. This formative work will also feed back into the delivery of lectures and tutorials.
Assessment Methods
The module is assessed through a Portfolio and an examination.
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Compulsory
Optional
