MATH219 - Statistics and Probability

Year

Credit points

Campus offering

Prerequisites

MATH107 Introduction to Logic and Algebra

Incompatible

STAT201 Statistics and Probability, STAT206 Introductory Statistics for Science

Teaching organisation

Unit rationale, description and aim

This unit provides an introduction to descriptive statistics, simple combinatorics and probability and their use in inferential statistics. Discrete and continuous distributions will be considered with a focus on the normal distribution. As well as sampling distributions and the examination of estimation and hypothesis testing including analysis of variance and some non parametric tests. Bivariate data analysis on quantitative data using regression and correlation and on qualitative data using cross-tabulations will also be introduced. Appropriate technology for statistical analysis will be used including graphics calculators and computer packages SPSS and Microsoft Excel. The importance of correct and ethical use of statistics will be discussed including references to real cases, including examples from the Aboriginal and Torres Strait Island perspective.

Learning outcomes

To successfully complete this unit you will be able to demonstrate you have achieved the learning outcomes (LO) detailed in the below table.

Each outcome is informed by a number of graduate capabilities (GC) to ensure your work in this, and every unit, is part of a larger goal of graduating from ACU with the attributes of insight, empathy, imagination and impact.

Explore the graduate capabilities.

On successful completion of this unit, students should be able to:

LO1 - Select appropriate statistical procedures for a variety of types of data sets. (GA4, GA5) 

LO2 - Analyse and critically evaluate data and use technology efficiently to solve problems. (GA4, GA5, GA7, GA8, GA10)

LO3 - Determine correct inferences from a variety of data sets. (GA3, GA4, GA5, GA8, GA9, GA10) 

LO4 - Understand basic concepts in probability and distributions and calculate and interpret probabilities in chance situations. (GA4, GA5, GA8, GA10) 

LO5 - Communicate a variety of statistical knowledge to others. (GA3, GA5, GA9, GA10) 

LO6 - Appreciate the role of ethical and valid use of statistics. (GA2, GA3, GA4, GA5) 

Graduate attributes

GA2 - recognise their responsibility to the common good, the environment and society 

GA3 - apply ethical perspectives in informed decision making

GA4 - think critically and reflectively 

GA5 - demonstrate values, knowledge, skills and attitudes appropriate to the discipline and/or profession 

GA7 - work both autonomously and collaboratively 

GA8 - locate, organise, analyse, synthesise and evaluate information 

GA9 - demonstrate effective communication in oral and written English language and visual media 

GA10 - utilise information and communication and other relevant technologies effectively.

Content

Topics will include: 

1. Exploratory data analysis in descriptive statistics. 
2. Introduction to probability, combinatorics and set counting techniques. 
3. Discrete probability distributions including binomial, Poisson and discrete uniform cases. 
4. Continuous distributions including uniform, exponential and normal distributions. 
5. Sampling distributions and Students t. 
6. Estimation in statistical inference. 
7. Hypothesis testing and errors. 
8. Analysis of Variance and Fisher’s F test. 
9. Nonparametric tests. 
10. Correlation and regression and analysis of qualitative bivariate data 
11. The Chi square distribution. 
12. Use and misuse of statistics 

Learning and teaching strategy and rationale

 As is common in Mathematics a variety of Active Learning strategies promote the best acquisition of skills and understanding. This allows students to learn the skills via Interactive Lectures, or suitable online strategies, and then build understanding, competence and confidence via (attendance) tutorials involving cooperative groups, peer review and other relevant strategies. In all cases this should be supported using available online technology. 

This unit will normally include the equivalent of 24 hours of lectures together with 24 hours of attendance mode tutorials. 

150 hours in total with a normal expectation of 48i hours of directed study and the total contact hours should not exceed 48 hours. The balance of the hours becomes private study. 

Assessment strategy and rationale

To successfully complete an undergraduate Mathematics sequence, students need an understanding of a variety of basic Mathematical topics and an ability to apply that understanding to a variety of problems. To succeed at problem solving in Mathematics, students must have a variety of skills at their fingertips from which to choose and an ability to recall those skills under some pressure. The assessment strategy chosen, while traditional, tests and supports student learning. The continuous assessment component helps reinforce learning and builds collaborative skills. The examination components ensures that students have fully integrated the learning and can bring a variety of strategies to bear under pressure. 

Typing of Mathematical notation either requires a significant investment of time, or knowledge of advanced Mathematical typesetting software. Neither of those skills are suitable for an undergraduate course in Mathematics. Consequently, assignments, tests and examinations are expected to be handwritten and so submitted as hardcopy, rather than through Turnitin. The expected tasks for this unit will all fit into this category. 

Overview of assessments

Representative texts and references

Bluman, A. (2017) Elementary Statistics- A step by step approach, 10th Edition. New York: McGraw-Hill 

De Veaux, R., Velleman, P. & Bock, D. (2015) Stats: Data and Models, New York: Addison Wesley 

Field, A. (2013) Discovering Statistics Using SPSS, Sage Publications 

Freedman, D., Pisani, R. & Purves, R. (2011) Statistics, 4th Edition. Viva Books 

Huff, D. (1991) How to Lie with Statistics, London: Penguin 

Pearl, J. (2009) Causality: Models, Reasoning and Inference, Cambridge: Cambridge University Press 

Salkind, N. (2016) Statistics for People Who (Think They) Hate Statistics: Excel 2007 Edition, Sage Publications