• Statistics

Statistics

Statistics is studied as part of the Mathematics and/or Further Mathematics A Level courses.  Usually S1 is taken as one module of the six-module Mathematics A level.  S2 may constitute one module either of Mathematics A level or of Further Mathematics at AS or at A level.  The examination board whose syllabus we follow is Edexcel; course books are those authorised by Edexcel and published by Heinemann, entitled simply S1, S2 and S3.

The material is assessed by examination only; there is no coursework.  Each module examination lasts one hour and 30 minutes: all questions are compulsory (so every part of the syllabus must be thoroughly studied). S1 and S2 examinations are set both on January and May/June; S3 is set only in June.

Statistics is an essential subject not only for mathematicians and scientists but especially for those wishing to do study in Economics, Psychology, Sociology and other social sciences.  It is an invaluable tool for those who want to pursue a career in Medicine, Biochemistry or other research disciplines: a good pure mathematician should foster his or her data-handling abilities in order to be able to read the research literature, let alone one day contribute to it.

Pre-requisites: to succeed with Statistics, a student will need not only good basic pure Mathematics skills and a high degree of accuracy in calculations but also a good level of written English.  This latter is necessary for comments, comparison and, above all, interpretation of numerical results.  Throughout the course, a good student will be prepared to repeat and improve written assignments until a piece of work with excellent accuracy, clarity and with graphical representation has been produced.

S1: The syllabus covers basic data-handling (measures of average, dispersion, skewness and graphical representations); probability (simple and conditional); techniques of correlation and regression; analysis of discrete random variables; and an introduction to the Normal distribution.

S2: Includes study of the Binominal and Poisson distributions; approximations to the discrete distributions by the use of the continuous Normal distribution; analysis of continuous Normal distribution; analysis of continuous random variables; and an introduction to simple hypothesis testing for Binominal and Poisson parameters.

S3: The S3 syllabus builds on what has been learned in S1 and S2. Here are found linear combinations of Normal variables, sampling techniques, from random to stratified; the chi-squared variable used both for goodness or fit tests and for contingency tables; tests for linear correlation and for rank correlation; and perhaps most importantly, study of the sampling distribution of the mean, leading to an introduction to confidence intervals and to hypotheses tests for the mean.