Pearson Edexcel Level 3 Advanced Subsidiary And Advanced .

Pearson Edexcel Level 3Advanced Subsidiary andAdvanced GCE in StatisticsStatistical formulae and tablesFor first certification from June 2018 for:Advanced Subsidiary GCE in Statistics (8ST0)For first certification from June 2019 for:Advanced GCE in Statistics (9ST0)This copy is the property of Pearson. It is not to be removed from theexamination room or marked in any way.P58394A 2017 Pearson Education Ltd.1/1/1/1/1/1/1/

Edexcel, BTEC and LCCI qualificationsEdexcel, BTEC and LCCI qualifications are awarded by Pearson, the UK’s largest awarding bodyoffering academic and vocational qualifications that are globally recognised and benchmarked.For further information, please visit our qualification website at qualifications.pearson.com.Alternatively, you can get in touch with us using the details on our contact us page atqualifications.pearson.com/contactusAbout PearsonPearson is the world’s leading learning company, with 35,000 employees in more than 70 countriesworking to help people of all ages to make measurable progress in their lives through learning. Weput the learner at the centre of everything we do, because wherever learning flourishes, so do people.Find out more about how we can help you and your learners at qualifications.pearson.comAll information in this document is correct at time of publication.ISBN 978 1 4469 4764 7All the material in this publication is copyright Pearson Education Limited 2017

Contents1234IntroductionAS Level in StatisticsA Level in StatisticsStatistical TablesTable 1: Cumulative Binomial Distribution FunctionTable 2: Cumulative Poisson Distribution FunctionTable 3: Normal Distribution FunctionTable 4: Percentage Points of the Normal DistributionTable 5: Percentage Points of the Student’s t-distributionTable 6: Percentage Points of the χ 2 DistributionTable 7: Percentage Points of the F-distributionTable 8: Critical Values of the Product Moment Correlation CoefficientTable 9: Critical Values of Spearman’s Rank Correlation CoefficientTable 10: Critical Values of the Wilcoxon Signed-Rank StatisticTable 11: Critical Values of the Wilcoxon Rank-Sum1248815171819202123242526

1IntroductionThe formulae in this booklet have been arranged by qualification. Students sitting AS Statistics papers shouldrefer to Section 2, pages 2 – 3. Students sitting A Level Statistics papers should refer to Section 3, pages 4 – 7.Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in StatisticsStatistical Formulae and Tables – Issue 1 – August 2017 – Pearson Education Limited 20171

2AS Level in StatisticsPopulation variance, σ2, x2 122 N μ N ( x μ) Population standard deviation, σ, x2 2 μ N 1( x μ )2 NSample variance 1 x2 n 1 ( x) 2n 1( x x )2 n 1Sample standard deviation 1 x2 n 1 ( x) 2n 1( x x )2 n 1Binomial probability calculations: n n xP ( X x ) p x (1 p ) x Mean npVariance np(1 p)For a random sample of nx observations from N ( μ, σ 2 )X μ N(0, N ( 0,1)1)σnTest statistic for a binomial proportion using normal distribution:pˆ pp (1 p )n2 N(0, N ( 0,1)1)Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in StatisticsStatistical Formulae and Tables – Issue 1 – August 2017 – Pearson Education Limited 2017

Product moment correlation coefficient:S xyr S xx S yy ( x x )( y y ){ ( x x ) } { ( y y ) }ii2i2 xi yi xi2 i( x ) ( y )i( x ) in2in y) ( 2 y2iin Coefficients for least squares regression line:least squares regression line of y on x is y a bx , wherea y bxthe regression coefficient of y on x is b S xyS xx ( x x )( y y ) (x x )ii2iTest for association: (Oi EiEi)2is approximately distributed as χ 2Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in StatisticsStatistical Formulae and Tables – Issue 1 – August 2017 – Pearson Education Limited 20173

3A Level in StatisticsPopulation variance, σ2, x2 122 N μ N ( x μ) Population standard deviation, σ, x2 2 μ N 1( x μ )2 NSample variance, s2, 1 x2 n 1 ( x) 2n 1( x x )2 n 1Sample standard deviation, s, 1 x2 n 1 ( x) 2n 1( x x )2 n 1Binomial probability calculations: n n xP ( X x ) p x (1 p ) x Binomial mean npBinomial variance np (1 p)For a random sample of nx observations from N ( μ, σ 2 )X μ N(0, N ( 0,1)1)σnTest statistic for a binomial proportion using normal distribution:pˆ pp (1 p )n4 N(0,N ( 0,1)1)Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in StatisticsStatistical Formulae and Tables – Issue 1 – August 2017 – Pearson Education Limited 2017

Product moment correlation coefficient:r S xyS xx S yy ( x x )( y y ){ ( x x ) } { ( y y ) }i i2i2 xi yi xi2 i( x ) ( y )i( x ) in2in y) ( 2 y2iin Coefficients for least squares regression line:least squares regression line of y on x is y a bx , wherea y bxthe regression coefficient of y on x is b S xyS xx ( x x )( y y ) (x x )ii2iBayes’ theorem for up to three events:()P Aj B ( ) ()iiP Aj P B Ajn P( A ) P(B A )i 1The Poisson probability formula:P ( X x) e λλxx!Poisson mean λPoisson variance λThe exponential cumulative probability formula:P(X x) 1 e λxExponential mean 1λExponential variance 1λ2E ( aX bY ) aE ( X ) bE (Y )Var ( aX bY ) a 2 Var ( X ) b 2 Var (Y ) , for independent variables X and YPearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in StatisticsStatistical Formulae and Tables – Issue 1 – August 2017 – Pearson Education Limited 20175

For a random sample of nx observations from N (μ, σ 2)X μ ttn–1n 1(also valid in matched-pairs situations)SnFor a random sample of nx observations from N (μx, σx2) and, independently, a random sample of nyobservations from N (μy , σy2)(X Y ) (μ μyxσ x2 σ nx n y2y) N(0,N ( 0,1)1)For a random sample of nx observations from N (μx, σx2) and, independently, a random sample of nyobservations from N (μy , σy2) where σx2 σy2 σ 2 (unknown)(X Y ) (μx μyS(n x)wherennx n–2x nyy 2 11 S p2 nx n y 2p) tt() 1 S x2 n y 1 S y2nx n y 2Test statistic for the difference in two binomial proportions:p1 p2where standard error standard errorwhere p 11 p (1 p ) n1 n2 p1 n1 p2 n2n1 n2Test for association and goodness of fit test: (Oi EiEi6)2is approximately distributed as χ 2Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in StatisticsStatistical Formulae and Tables – Issue 1 – August 2017 – Pearson Education Limited 2017

Analysis of variance (one-way and two-way):one-factor model xij μ αi εij , where εij N (0, σ2)total sum of squares SST xij2 ijbetween groups sum of squares SS B T2nTi 2 T 2 i n nitwo-factor model (with m rows and n columns)xij μ αi βj εij , where εij N (0, σ2)total sum of squares SST xij2 ijbetween rows sum of squares SS R T2mnRi2 T 2 i n mnbetween columns sum of squares SSC C 2j mj T2mnCohen’s d formula:d (x1 x2 )swhere s (n1 1) s12 ( n2 1) s22n1 n2 2Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in StatisticsStatistical Formulae and Tables – Issue 1 – August 2017 – Pearson Education Limited 20177

4Statistical TablesTable 1: Cumulative Binomial Distribution FunctionThe tabulated value is P(X x), where X has a binomial distribution with parameters n and p.p0.01x012n 00n 3n 01.00001.00001.00001.00001.0000n 000n 01.0000n .00001.00001.0000n 00001.00001.00001.0000Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in StatisticsStatistical Formulae and Tables – Issue 1 – August 2017 – Pearson Education Limited 5678

p0.01x0123456789n n 10x01234567891011n 11x0123456789101112n 0.75350.63310.50001.00001.0000

Pearson Edexcel Level 3 Advanced Subsidiary and Advanced GCE in Statistics Statistical formulae and tables For first certification from June 2018 for: Advanced Subsidiary GCE in Statistics (8ST0) For first certification from June 2019 for: Advanced GCE in Statistics (9ST0) This copy is the property of Pearson. It is not to be removed from the