Module Identifier | MA12410 | ||

Module Title | BASIC DESCRIPTIVE STATISTICS AND PROBABILITY | ||

Academic Year | 2000/2001 | ||

Co-ordinator | Dr J A Lane | ||

Semester | Semester 1 | ||

Pre-Requisite | A or AS level Mathematics or any of MA12010, MA12510, MA12610 taken at the same time. | ||

Mutually Exclusive | May not be taken at the same time as, or after, any of MA10020 to MA11410. | ||

Course delivery | Lecture | 22 x 1 hour lectures | |

Seminars / Tutorials | 6 x 1 hour example classes | ||

Assessment | Exam | 2-hour written examination | 100% |

Resit assessment | 2-hour written examination | 100% |

**General description**

This module starts with the descriptive statistics used for summarising and displaying data. It then introduces probability, the mathematical language of uncertainty and discusses the analysis of data in commonly occurring situations.

**Aims**

To introduce students to basic ways of thinking about data. To give students the methodology for summarising and interpreting data. To introduce the basic ideas of probability, random variable, probability distributions, expectation and variance.

**Learning outcomes**

On completion of this module, a student should be able to:

- categorise, summarise and interpret various types of data;
- explain the concept of probability;
- deduce probabilities in a variety of simple symmetric situations;
- solve elementary combinatoric problems;
- explain the concept of random variable;
- explain the concept of probability distribution and density;
- describe a variety of standard distributions;
- use probability tables or a calculator for finding probabilities associated with a variety of standard distributions;
- deduce important `features? of some standard distributions;
- model stochastic situations with standard distributions;
- explain the concepts of expectation, variance and standard deviation and deduce them in familiar standard and simple unfamiliar situations;
- manipulate simple expressions involving expectations;
- explain the Central Limit Theorem and its significance;
- determine when it is appropriate to approximate a Binomial distribution by a Normal distribution and do this using the `continuity correction?.

**Syllabus**

1. SUMMARISING DATA: Categories of data, frequency tables, descriptive statistics, histograms, stem and leaf plots, comparing data sets.

2. PROBABILITY: Axioms of probability, deduction in symmetric situations, classical sample space.

3. COMBINATORICS: Basic formulae with applications.

4. THE ALGEBRA OF SETS: Basic formulae with applications.

5. CONDITIONAL PROBABILITY: Definition, the chain rule, Bayes rule, applications.

6. PROBABILITY DISTRIBUTIONS: Discrete and continuous cases, the probability mass function, the density function, calculation of probabilities, distribution functions, standard distributions, use in modelling. Calculation of probabilities using Statistical Tables.

7. EXPECTATION: Definitions of expectation, variance and standard deviation; properties, calculation in specific cases.

8. THE CENTRAL LIMIT THEOREM: Statement, significance, applications, approximation of the Binomial distribution by the Normal distribution.

[Note: concepts and methodology are illustrated throughout by means of a wide variety of specific examples.]

**Reading Lists**

**Books**
**** Should Be Purchased**

J Murdoch & J A Barnes.
*Statistical tables*. Macmillan

M R Spiegel.
*Theory and Problems of Probability & Statistics. Schaum's Outline Series*. McGraw-Hill
**** Recommended Text**

N A Weiss.
*Elementary Statistics*. 2nd. Addison-Wesley
**** Supplementary Text**

P T Strait.
*A first course in Probability & Statistics with applications*. 2nd. Harcourt Brace Jovanovich

P G Hoel.
*Elementary Statistics*. 4th. John Wiley