6.2 Statistics Syllabus 2006 - 2007
Textbook: A Concise Course in A Level Statistics (Fourth Edition). The book references for 62 are from the 3rd edition. The 4th edition has some useful information on the use of Excel which should be read. 62 groups will study just S2.
Past and specimen papers and solutions for the new modules are available as are copies of the Heinemann textbooks which have been written by authors from London Board.
These notes should be read in conjunction with the S2 and syllabus which include further detail on what is required for each topic. The specific questions suggested are only a guide.
The white file in W13 titled Teaching Activities Resource Pack by the Royal Statistical Society has some useful project ideas which use I.T.
The OUP book ‘Practical Exercises in Applied Statistics’ is a useful source to make the theory more relevant.
Use of IT, graphic calculators etc. All teachers should make use of IT, graphic calculators etc., the notes indicate certain places where IT must be incorporated into teaching; this should be regarded as a minimum provision. IT Resources include an OHP view screen of the CASIO 9750 graphic calculator. In particular all pupils must be shown how to make efficient use of the statistics functions on their calculators and how to use spreadsheets (Microsoft Excel) for the calculation of statistics. In general it is no longer necessary to produce tables when calculating means, standard deviations etc. when this can be done on a calculator; solutions should however include details of ∑ x , ∑ x2 etc.
Order | Topic | Textbook Ref | Syllabus reference | Notes |
1 | S2 syllabus Data collection. | Hand out sheet on sampling. Chapter 8 pages 462 to465 | S2 (4) Collection of data Sample and population. Sampling units, sampling frame census. Collection of sample data. | Reference should be made to the importance of this topic in project work of any kind. It may be easier to do this section later on in the course. |
2 | Binomial, (Geometric), Poisson, Distributions. | Chapter 5 Page 260 Ex5a Q1,3,5,7,8, 17&19 (use logs) 5b Q1 – 5, 5c Q1 5e Q1&2, 5f Q2&3 (5g Q4&9), 5i Q1 - 6 5j Q1,3,5&6 5l Q3, 5m Q1 - 3 5n Q11,12&25 | S2(1) Discrete distributions The discrete, binomial and Poisson distributions. The mean and variance of the binomial and Poisson distributions. The use of the Poisson distribution as an approximation to the binomial distribution. | The number of Red Wine Gums –B(12,0.2) Use Cumulative probability tables on pages 632 and 633. DO NOT use recurrence formulae. The Geometric distribution is optional |
3 | Continuous Random Variables. | Chapter 6 Page 315 Ex6a Q1,3,5&6 6b Q2,3,5,9&10 6c Q6,7&8 6d Q8,9,13&14 6e Q1,2&4 6h Q5,6&12 | S2(2) Random variables (Continuous ) The idea of a continuous random variable. The probability density function and the cumulative distribution function for a continuous random variable. Relationship between density and distribution functions. Mode and median for continuous random variables. Mean and variance of a random variable. Concept of expectation. Mean of a linear combination of two random variables. Variance of a linear combination of two random variables when the variables are independent. | Exponential Functions are not on the syllabus. |
4 | Uniform and Normal Distributions. | Chapter 6 page 349 Ex6f Q1 - 6 Chapter 7 7j Q4 - 8 7k Q2,5,6 & 20 | S2(3) Continuous distributions The continuous uniform (rectangular) distribution. The Normal distribution, including mean, variance and cumulative distribution function. Use of the Normal distribution as an approximation to the binomial and the Poisson distributions, with the application of the continuity correction. | Revision of Normal Distribution from S1 |
5 | Hypothesis tests | Chapter 8 page 438 Ex 8e 3,4(optional) 8f 2,4,6 8g 1,3,5,6,7,11 8h 1,2,4,5 Chapter 10 page 539 Ex 10g 3,5 10i 2,4,6 | S2 (4)Concepts of a statistic and its sampling distribution Concept and interpretation of a hypothesis test. Null and Alternative hypotheses. Critical region. One-tailed and two tailed tests. Hypothesis tests for the parameter b of a binomial distribution and for the mean of a Poisson distribution. | Use of hypothesis tests for refinement of mathematical models. Use of a statistic as a test statistic, Use of tables to carry out tests as well as calculation of cumulative probabilities. |
THE S2 SYLLABUS HAS NOW BEEN COMPLETED |
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