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6.1 Statistics
Sixth Form Statistics Syllabus 2006 - 2008 Textbook: A Concise Course in A Level Statistics (Fourth Edition) The book references are from the 4th edition. The 4th edition has some useful information on the use of Excel which should be read. Yr 12 will be studying for OCR AS Module 4732 Probability and Statistics 1 (S1) Half the syllabus will be taught in Yr 12 and the rest completed in Yr 13 . The external module will be taken in January 2008. All Yr 13 will be studying the rest of AS Module 4732(S1). This external module will be taken in January 2006. Students opting for OCR A2 Module 4733 Probability and Statistics 2 (S2) will take this exam in June 2007. Since A Level is now to be accessible from level 7 of the National Curriculum and all our pupils have been taught far more than this, some of the material in S1 will have been covered in years 10 and 11; however, care will be needed in sets which contain boys new to the school. Past and specimen papers and solutions for the new modules are available as are copies of the Cambridge(OCR) textbooks which have been written by authors from the boards. These notes should be read in conjunction with the S1 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 Ststistical Society has some useful project ideas which use I.C.T. The OUP book ‘Practical Exercises in Applied Statistics’ is a useful source to make the theory more relevant. All teachers should make use of ICT, graphic calculators etc., the notes indicate certain places where ICT should be incorporated into teaching ; this should be regarded as a minimum provision. ICT 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 (Notes by AVM are available) Students should also know 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 must however include details of ∑ x , ∑x2 etc Order | Topic | Page References | Syllabus Details | Notes | 1. . | Representation of Data (e) 2doubles September | P28 -46 Ex 1f p44 1a,b,2,3,4,8,9,10 | (e) calculate the mean and standard deviation of data(including grouped data) either from the data itself or from given totals such as ∑ x , ∑ x2. | Include variance. (∑( x-a), and ∑ (x-a)2 Coding to be done later) | 2. | Probability (d),(e),(f) 1 single 3 doubles September, October | P168 -197 Ex 3a p173 (odd) Ex 3b p 181(even) Ex 3c p 192(even) Ex 3d p200 A1,2,3,5,6 P201 B1,2,6,14 | (d) evaluate probabilities in simple cases by means of enumeration of elementary events(eg for the total score when two fair dice are thrown) . (e) use addition and multiplication of probabilities, as appropriate, in simple cases. (f) understand informally the meaning of exclusive and independent events, and calculate and use conditional probabilities in simple cases eg situations that can be represented by means of a tree diagram. | No need for calculations involving perms and combs this year. | 3. TEST | Discrete Random Variables (a) 3 doubles October TEST middle of November | P233-251 Ex 4a p236 1,2,4,6 Ex 4b p244 1,2,6,12 Ex 4cp251 1,5,7,8,9,16,18 | (a) construct a probability distribution table relating to a given situation involving a discrete random variable X and calculate the expectation, variance and standard deviation of X (the notations E(X) for expectation (also referred to as expected value or mean) and Var(X) for variance , are included) | Avoid questions involving (aX+b) | 4. | Discrete Random Variables (b),(c),(d) (Geometric) and Binomial Distributions 3 doubles on Binomial (1double,1single on Geometric if time) January | P 270-290 Ex 5a p276 2,3,4,5,6,7,13,15 Ex 5b p285 1-9,12 Ex 5c p290 1-5,7,14 Ex 5g p307 8,9,11,14,16 | (b) use formulae for probabilities for the binomial and geometric distributions ,and model given situations by one of these, as appropriate(the notations B(n.p) and Geo(p) are included) (c) use tables of cumulative binomial probabilities(or equivalent calculator functions). (d)use formulae for the expectation and variance of the binomial distribution, and for the expectation of the geometric distribution. | Practicals involving tubes of wine gums (i)X is the number of trials to obtain a red where the model is Geo(.0.2) (ii)X is the number of reds obtained in a tube where the model is B(12,0.2) | Year 13 | The S1 syllabus to be continued by all | External Exam January 2006 | | | 1 | Representation of Data a,b,c,d,e Coding Cumulative Fr Curves Skewness Boxplots and Outliers | P56-57 Ex 1i p58 P75-78 Ex1k p81q7,9 P84-90 Ex1l p90q4,6,8,10 P92-99 Ex1mp99q2,3,6,7,8 | Calculate the mean and sd of a set of data including the use of ∑( x-a), and ∑ (x-a)2 Include the mean distance or mean absolute deviation from mean Express conclusions verbally Revise Histograms and Stem and leaf Use Quartiles for skewness and Outliers | OCR Stats 1 p54 Linear Interpolation not needed Summary p102-105 Mixed test 1B p116 | 2 | Bivariate Data Scatter Diagrams, Regression Correlation i)pmcc ii)Spearmans | P118-136 P136 Ex 2a q2,3,5,6,11,13 P139-142,144 Ex 2b p145 q2,3,6 P146-151 Ex 2c p1512,3,8,10,11,14 | (e)Understand the difference between an independent or controlled and dependent var. (f) From raw data or summarised data the equation Least squares and regression lines (g)Calculate of a regression line for both y on x and x on y and know both lines pass through the mean centre (x,y). (h) Select appropriate line and interpret (a)Calculate the product moment correlation coefficient for bivariate data. (d)Know that the coeff.corr. is unaffected by coding(Linear transformation) of variable. (b) Spearmans coeff. of rank correlation (c)Interpret correlation in relation to scatter diagram and closeness of coeff.to -1,0,1 | See p176/7 OCR S1 for ∑ d2 calculations. Use Sxx, Sxy see formulae book. Also worth doing are the practicals P185 Heights of Parents and Children P190 Hooke`s Law P157 OCR S1 Do p162 q4 All this work needs efficient use of calculators. | 3 | Probability Permutations and Combinations | P206-218 Ex 3f p219 1-20 Also Ex 4f p266 q2,9,10 | (a)Perms and combs. (b) Selections (c)Arrangements with repetition and restrictions | | 4 | Discrete Random Variables Geometric and revision | Ex 5a p276 q2,3,4,5,6,7.13 Ex 5g p307 q8,9,11,14,16 | S1 is now complete | |
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