MTH0004 - Foundation Statistics (2023)

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MODULE TITLEFoundation Statistics CREDIT VALUE15
MODULE CODEMTH0004 MODULE CONVENERDr Chaitra H. Nagaraja
DURATION: TERM 1 2 3
DURATION: WEEKS 11 0 0
Number of Students Taking Module (anticipated) 30
DESCRIPTION - summary of the module content

In this module you will earn an understanding of statistical modelling and how it is used to help us understand and predict the world around us. Statistics is the study and analysis of data which is usually applied to a scientific problem in order to draw conclusions about a population. In this module you will learn about mathematical models in probability and statistics; correlation and regression; inference and comparison of models; discrete and continuous distribution; sampling and hypothesis testing to statistical modelling. You will apply the theory to analyse and draw conclusions from a range of real-world data sets. The module will provide you with skills bridging the gap between the material covered prior to a university level and that of a first year degree programme. 

You will have weekly scheduled sessions led by the module instructor/convenor. During those sessions you will be introduced to the topic through lecture presentations, learning materials, worked examples provided exercise worksheet, and computer lab practicals. In this module you will learn how to: , analyse and interpret data using R; capply and present probability distributions for discrete and continuous random variables; perform sampling and hypothesis testing; present findings and communicate results in a coherent way. You will be assessed through a combination of summative assessments:  2 online reports, a test, and a final exam.     

AIMS - intentions of the module

The module aims to develop key ideas and techniques in probability, statistics and data analysis, which will provide you with the necessary foundation for any quantitative degree programme. It helps you build a thorough understanding of statistical inference by getting a grasp of the underlying theories concepts and statistical/mathematical procedures. This will enhance your performance at any research or job prospect which involves statistical reasoning and investigations.

 

INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)
Module Specific Skills and Knowledge:
1 Demonstrate a sound understanding of selected essential topics in probability theory
2 Demonstrate an ability to implement theoretical concepts to describe and predict real-world problems;
3 Demonstrate a knowledge of the basic ideas of statistical inference, including probability distributions, point and interval estimation and hypothesis testing;
 
Discipline Specific Skills and Knowledge:
4 Show sufficient knowledge of fundamental mathematical and statistical concepts, manipulations and presentation of results.
5 Demonstrate an appreciation of inferential statistical concepts and predicted outcomes
 
Personal and Key Transferable/ Employment Skills and Knowledge:
6 Be able to provide thorough reasoning using abstract ideas, and to formulate and solve problems; 
7 Be able to communicate results and solutions effectively orally and in writing;
8 Use learning resources appropriately;
9 Exhibit self-management and time management skills.
 
SYLLABUS PLAN - summary of the structure and academic content of the module
  • Representation of data: histograms, box plots, bar graphs; measures of location (mean, median, mode); measures of dispersion (variance, standard deviation, and interquartile range); skewness and concepts of outliers.
  • Probability: sample space, mutually exclusive and complementary events, conditional probability, Bayes' Theorem; independence of events; addition and multiplication rules, using a Venn and tree diagrams; sampling with and without replacement.
  • Correlation: scatter plot, product moment correlation, interpretation of a scatter plot
  • Random variables: probability mass function, cumulative distribution function, probability density function, mean and variance of random variables, discrete uniform distribution, binomial distribution, Poisson distribution, normal distribution, t distribution, normal approximation to the binomial distribution, normal approximation to the Poisson distribution, density histogram.
  • Hypothesis testing: one-sample t-test for mean, confidence interval, Type I error, Type II error, null and alternative hypotheses.

 

LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
Scheduled Learning & Teaching Activities 44.00 Guided Independent Study 106.00 Placement / Study Abroad 0.00
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
Category Hours of study time Description
Scheduled learning & teaching activities 22 Formal lectures of new material
Scheduled learning & teaching activities 11 Seminars and tutorials, worked examples, with individual and group support
Scheduled learning & teaching activities 11 Computer Lab Practical
Guided Independent Study 106 Lecture & assessment preparation, wider reading.

 

 

ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
Form of Assessment Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Weekly exercises 10 x 1 hour 1-9 Exercises discussed in class, solutions provided

 

SUMMATIVE ASSESSMENT (% of credit)
Coursework 50 Written Exams 50 Practical Exams 0
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Test  15% 1 hour 1-9 Electronic
2 Reports

1 x 15%

1x 20%

 Short report essay 1-9 Electronic/annotated
Written Exam 50% 2 hours 1-9 Annotated scripts

 

DETAILS OF RE-ASSESSMENT (where required by referral or deferral)
Original Form of Assessment Form of Re-assessment ILOs Re-assessed Time Scale for Re-assessment
Test Test 1-9 Referral/deferral period
2 Reports/Online Short report essay 1-9 Referral/deferral period
Written Exam Written Exam 1-9 Referral/deferral period

*(each online quiz (2 in total) may be attempted multiple times, but students are required to achieve at least 60% for each quiz - otherwise a score of zero will be recorded.)

RE-ASSESSMENT NOTES
Deferral – if you have been deferred for any assessment, you will be expected to complete relevant deferred assessments as determined by the Mitigation Committee. The mark given for re-assessment taken as a result of deferral will not be capped and will be treated as it would be if it were your first attempt at the assessment.
 
Referral – if you have failed the module overall (i.e. a final overall module mark of less than 40%) you will be required to undertake re-assessments as described in the table above for any of the original assessments that you failed. The mark given for a re-assessment taken as a result of referral will be capped at 40%.
RESOURCES
INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener

Basic reading\Web-based and electronic resources:

  • ELE – College to provide hyperlink to appropriate pages

Other resources:

  • ‘Probability’ by McColl, J. H., London: Edward Arnold, 1995 [Library]
  • ‘Statistics’ by Mayer, A. D. and Sykes, A. M., Arnold, 1996 [Library]

 

Reading list for this module:

There are currently no reading list entries found for this module.

CREDIT VALUE 15 ECTS VALUE 7.5
PRE-REQUISITE MODULES None
CO-REQUISITE MODULES None
NQF LEVEL (FHEQ) AVAILABLE AS DISTANCE LEARNING No
ORIGIN DATE Thursday 29 July 2021 LAST REVISION DATE Thursday 07 December 2023
KEY WORDS SEARCH Statistics; mathematics; probability; data; analysis; modelling; inference.