# Module – Introduction to Probability & Statistics

FHEQ Level: Level 3 (Foundation Year)
Credits: 20
Module Code: G300 00001
Course Reference Number (CRN): 52785
Delivery: September Start, Trimesters 1&2 (Long Thin)

#### Syllabus Outline

• Basic statistics: mean, median, mode, standard deviation and variance, quartiles
• How to load data and compute basic statistics from those data using “R programming language”
• Statistical graphs and their interpretation: bar plots, stem-and-leaf diagrams
• Compute confidence interval: understand confidence intervals and z-scores table
• Properties of probabilities plus probability mass/density function, probability cumulative function
• Understand the concept of sample space, law of total probabilities, Bayes’ theorem and their applications
• Draw the graph of a given probability distribution
• Application of combinatorics to probabilities (how to compute the number of possible combinations of objects)
• Expectation and variance of random variables
• Properties of variance and different ways to compute variance
• Relationship between variance of a random variable and its mean
• Hypothesis testing (z-score test, t-test)
• Apply statistical tests to problems involving the comparison of two populations
• Basic understanding of central limit theorem
• Nonparametric statistics (Wilcoxon rank-sum test)

#### Assessment

Coursework: Core skills 1, 50%
Coursework: Core skills 2, 50%
More detailed information may be found in the Assessments section.

#### Texts

Introduction to statistics. By Ronald E Walpole. New York: Macmillan; London.

Probability & Statistics for Engineers & Scientists. By Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers, Keying Ye. Pearson; 9th edition.

Multivariate Data Analysis. By Joseph F. Hair Jr, William C. Black, Barry J. Babin, Rolph E. Anderson. Pearson; 7th edition.

Probability and Statistics for Engineers and Scientists. By Anthony J. Hayter. Duxbury Press; 4th edition.

Applied Statistics and Probability for Engineers. By Douglas C. Montgomery and George C. Runger. John Wiley & Sons; 6th edition.

Further updates and supplementary texts may be found in the University Reading Lists system.

#### Description

​This module concentrates on the introduction of statistics and probability skills required in mathematics, science and engineering. You will develop knowledge and the ability to develop the methodologies and modelling for real problems and learn the use of appropriate software packages. The relationship between the various aspects of this module and their role to mathematicians, scientists and engineers in the workplace will be highlighted.

#### Aims

1. To provide a level of knowledge, understanding and competence in basic mathematics to allow progression onto a technical or scientific degree.
2. To develop analytical and numerical problem-solving skills in basic mathematics.
3. To gain knowledge of specific software packages used to statistically analyse data.

#### Knowledge & Understanding

On successful completion of this module, you will be able to:

1. Understand and correctly interpret data and scientific and statistical graphs.
2. Distinguish between and apply different hypothesis testing models.
3. Provide a description of the statistical method used for data analysis, including a discussion of advantages, disadvantages, and necessary assumptions.
4. Communicate mathematical and statistical information effectively.
5. Be able to apply specialised software packages to statistically analyse data.

#### Learning, Teaching and Assessment

The module comprises of:

46 hours of lectures which are a blend of teacher-centred delivery of important concepts, flipped-classroom and learner-centred delivery for application of concepts in problem solving.

23 hours of problem-solving tutorial classes in which students embark on assisted problem-solving exercises.

A portfolio of formative tests in combination with set exercises will lead to final a final piece of summative coursework at the end of each trimester.