Statistics
ST237: Introduction to Statistical Data and Probability (5 ECTS)
This course discusses the nature of statistical data and the use of probability to describe random phenomena. Topics covered include: data sources, data presentation, numerical and graphical summaries, basic ideas of probability, conditional probability and indpendence, random variables, standard discrete distributions, mean and variance, joint distributions, and an introduction to the normal distribution.
Taught in Semester(s) I. Examined in Semester(s) I.
Workload: 24 hours (24 Lecture hours).
Module Learning Outcomes.
On successful completion of this module the learner should be able to:
- Construct appropriate graphical summaries for a sample of data, including stem-and leaf plots, dot-plots, box-plots. Calculate numerical summaries for a sample of data, including the mean and variance, median and quartiles. Use simple counting and combinatorial arguments to calculate probabilities. Calculate probabilities for combinations of events, including unions, intersections and complements, using the laws of probability. Calculate conditional probabilities and use Bayes theorem to reverse conditioning. Construct probability distributions for random variables in simple settings. Calculate means and variances of random variables. Calculate marginal and conditional distributions of bivariate discrete distributions, calculate the correlation, assess independence.
- Calculate probabilities from standard distributions (Binomial, Poisson, Normal) using tables.
- Use Minitab to explore data both numerically and graphically and to calculate probabilities from standard probability models.
Indicative Content
This module provides a basic introduction to the ideas of probability and how simple probability models can be applied in a number of contexts. The topics covered in the module are:
- Sources of data, sampling, experiments, random variation
- Exploring data - graphical and numerical summaries
- Basic notions of probability - sample spaces, events, combination of events, counting
- Conditional probability and independence, Bayes' Theorem
- Random variables and probability distributions
- Binomial and related probability distributions
- Poisson distribution for counts, events over time
- Expectation - mean and variance
- Bivariate distributions - marginal and conditional probabilities, correlation and independence
- Normal distribution - properties, use of tables, central limit theorem and approximations
- Use of Minitab for data exploration and probability model calculations
Module Resources
- Bluman, A. 2003. Elementary Statistics - a step by step approach. McGraw Hill.
- Hinde, J, & Newell, J. (compilers) 2004. Introduction to Probability and Statistics by DeVeaux & Velleman, Pearson Custom Publishing
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