MDA511 - Mathematical and Statistical Methods
Credit Points: 20 credit points
Workload: 60 hours
Aims & Objectives
This is a core unit out of a total of 12 units in the Master of Data Analytics (MDA). This unit addresses the course learning outcomes and complements other units in a related field by developing students’ specialised knowledge of statistical tools and technologies. For further course information refer to: http://www.mit.edu.au/study-with-us/programs/master-data-analytics. This unit is part of the AQF level 9 (MDA) course.
Students will be exposed to applied statistical methodologies from an analysis of data viewpoints. Statistical methods play an important role in analysing data in a useful form. To understand and interpret data, it is necessary to engage students with the fundamentals of statistics, statistical data investigations, probability, and hypothesis testing. Students will engage with not only statistical concepts, but also their application and interpretation using statistical tools, such as R.
This unit will cover the following topics:
- Linear Algebra
- Vectors, Scalars, Matrices
- Descriptive Statistics
- Probability and Discrete Probability Distributions
- Continuous Probability Distributions
- Estimation and Hypothesis Testing
- Inference and Population Variances
- Test of Goodness of Fit and Independence
- Statistical Optimisation Techniques
4.1 Course Learning Outcomes
The Course learning outcomes applicable to this unit in respect of the course being studied are listed on the Melbourne Institute of Technology website: www.mit.edu.au
4.2 Unit Learning Outcomes
At the completion of this unit students should be able to:
- Develop knowledge and skills in using statistics to interpret data.
- Analyse and evaluate probability for reasoning in real-world situations.
- Compare solutions to problems using appropriate statistical tools.
- Analyse and interpret results from descriptive and predictive data analysis.
- Apply optimisation techniques for given statistical data.
This unit will cover the content below:
|Week #||Lecture Topic||Laboratory and PBL Tutorial|
|1||Functions and Models||Practice Working with Numbers|
|2||Limits and Derivatives||Visualise Data with Graphs/Functions|
|3||Differential Calculus and Optimization||Explore Algebra and Symbolic Math|
|4||Integral Calculus||Solving Calculus Problems|
|5||Linear Algebra Fundamentals||Represent Linear Systems with Vectors and Matrices|
|6||Probability and Probability Distributions||Compute Probabilities and Probability Distributions|
|7||Conditional Probability and Bayes Rule||Apply Conditional Probability and Bayes Rule|
|8||Sampling and Confidence Interval Estimation||Evaluate Sampling and Estimate Confidence Interval|
|9||Hypotheses Testing||Perform Hypothesis Generation and Testing|
|10||Linear Regression: Estimating Relationships||Work with Linear Models|
|11||Time Series Analysis and Forecasting||Analyse Time Series Data|
* The Python language will be used in laboratory practices.
|Assessment Task||Due Date||Release Date||A||B||Learning Outcomes Assessed|
|Assignment 1 A (Formative)||Week 3||Week 1||5%||a|
|Assignment 1 B (In-class Test)||Week 6||Week 1||10%||a-b|
|Assignment 2||Week 11||Week 7||25%||c-d|
|Laboratory and Problem Based Learning participation & submission||Week 2-11||Week 1||10%||a-e|
|Final Examination (3 hours)||50%||a-e|
Task Type: Type A: unsupervised, Type B: supervised.
Contribution and participation (in class) (10%)
Students are expected to attend each scheduled session, arrive on time and remain for the entire session. Adherence to this requirement will be reflected in the marks awarded for this assessment. Students are also strongly encouraged to actively participate in the class discussions and tutorial activities by answering questions, expressing their opinions, insights and their learnings from the course.
Presentations (if applicable)
For presentations conducted in class, students are required to wear business attire.
Textbook and Reference Materials
- R. Peck, T. Short, Introduction to Statistics and Data Analysis, Cengage Learning, 6th Ed., USA, 2019.
- M. Taboga, Lectures on Probability Theory and Mathematical Statistics, CreateSpace Independent Publishing Platform, 3rd Ed., 2017.
- P. Bruce, A. Bruce, Practical Statistics for Data Scientists, 50 essential concepts, O’Reilly, 1st Ed., 2017.
- G. James, D. Witten, T. Hastie, R. Tibshirani, An Introduction to Statistical Learning with Application in R, Springers, 1st Ed., New York, USA, 2017.
- B. Cronk, How to use SPSS, A Step-by-Step Guide to Analysis and Interpretation, Routledge, London, 9th Ed., USA, 2017.
- L. C. Onyiah, Design and Analysis of Experiments. Classical and Regression Approaches using SAS, CRC 2016.
- T. J. Quirk, Excel 2016 for Engineering Statistics. A Guide to Solving Practical Problems, Springer 2016.
Adopted Referencing Style: IEEE. For IEEE Style referencing guidance go to: https://library.mit.edu.au/referencing/IEEE
MIT is committed to ensure the course is current, practical and relevant so that graduates are “work ready” and equipped for life-long learning. In order to accomplish this, the MIT Graduate Attributes identify the required knowledge, skills and attributes that prepare students for the industry.
The level to which Graduate Attributes covered in this unit are as follows:
|Ability to communicate||Independent and Lifelong Learning||Ethics||Analytical and Problem Solving||Cultural and Global Awareness||Team work||Specialist knowledge of a field of study|
|Levels of attainment||Extent covered|
|The attribute is covered by theory and practice, and addressed by assessed activities in which the students always play an active role, e.g. workshops, lab submissions, assignments, demonstrations, tests, examinations.|
|The attribute is covered by theory or practice, and addressed by assessed activities in which the students mostly play an active role, e.g. discussions, reading, intepreting documents, tests, examinations.|
|The attribute is discussed in theory or practice; it is addressed by assessed activities in which the students may play an active role, e.g. lectures and discussions, reading, interpretation, workshops, presentations.|
|The attribute is presented as a side issue in theory or practice; it is not specifically assessed, but it is addressed by activities such as lectures or tutorials.|
|The attribute is not considered, there is no theory or practice or activities associated with this attribute.|