Sigma Statistics NCEA Level 3 (4e)

The sections on Achievement Standards 3.10, 3.11 and 3.12 provide ground-breaking coverage of the ultimate stages of the statistics enquiry cycle approach. The emphasis is on statistical inference and interpretation rather than on statistical calculation. These chapters feature statistical methods such as bootstrapping, randomisation, resampling and experimental design (treatment and response variables, allocation of treatments, etc.), all of which are new in the Year 13 classroom. There is also a comprehensive selection of statistical reports, giving students the opportunity to practise critiquing causal-relationship claims and interpreting margins of error.

Technology is tightly integrated into the coverage, and features the new iNZight and Visual Inference Tools (VIT) software developed by Professor Chris Wild and his pioneering team at the University of Auckland, as well as the use of CAS calculators, spreadsheets and apps, where appropriate.

There are still plenty of investigations and puzzles to motivate students and stimulate thinking. These are both independent of, and related to, the coursework.

Full and comprehensive answers are provided.

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The NCEA Level 3 Mathematics and Statistics Achievement Standards for Year 13
Foreword to students, parents and teachers
Investigations
Puzzles
CAS calculator applications 
Spreadsheet activities 
Data sets 
Simulations 

3.8 Time series
1 Features of time series
2 Time-series analysis 
3 Seasonal adjustments and index numbers 

3.9 Bivariate measurement data 
4 Analysing bivariate data 
5 Bivariate relationships 

3.10 Trigonometric relationships 
6 Exploratory data analysis 
7 Sampling variability 
8 Differences between samples

3.11 Statistical experiments 
9 Types of experiment 
10 Experimental procedures

3.12 Statistically based reports 
11 Reading statistical reports for understanding 
12 Data sources 
13 Using data: analysis and inference 
14 Interpreting statistical reports

3.13 Probability concepts 
15 Probability and events based on chance
16 Probability techniques 
17 Conditional probability 
18 Arrangements and selections

3.14 Probability distributions 
19 Discrete random variables 
20 Using distributions to model probability
21 Binomial distribution 
22 Poisson distribution 
23 Normal distribution 
24 Simulation 
25 Combining distributions and random variables

Appendices
Appendix 1: Using the Central Limit Theorem to construct confidence intervals 
Appendix 2: Statistical and mathematical proofs 
Appendix 3: Formulae 
Appendix 4: Statistical tables

Answers
Index

• Bootstrapping – new statistical technique for developing informal confidence intervals for the median, and mean
• Randomisation – new statistical technique for assessing the significance of experimental results
• Seamlessly integrated with the new iNZight and Visual Inference Tools (VIT) software
• Numerous new and updated datasets for time series, bivariate data analysis, statistical inference and experiments
• Wide-ranging selection of statistically based reports – all in one place!
• Full coverage of experimental design – the types of blocking, controls, treatments, means effects and more!
• Specially commissioned new apps – a boxplot generator that superimposes the informal confidence interval, interactive apps for exploring the effect of parameter changes on the binomial, Poisson and normal distributions
• Risk and relative risk
• Inclusion of discussion about deterministic and probabilistic models
• New simulations
• New interactive spreadsheets
  

David Barton was born in New York and educated at Wellington College and Victoria University of Wellington, where he was awarded a Senior Scholarship and graduated with a BA (Hons). He was Assistant HOD Mathematics at Rangitoto College, and has been Chief Examiner for NZEST Scholarship in Mathematics with Statistics. An award-winning mathematics author, David first wrote the original edition of Sigma Mathematics in 1985 and, since then, has authored a stream of best-selling mathematics textbooks and workbooks in New Zealand and Australia.

Claire Laverty was brought up and educated in Dunedin, where she has been teaching mathematics since 1999. She graduated with a degree in mathematics and music from the University of Otago. A participant on the writing panels for the new mathematics and statistics curriculum, Claire is particularly interested in assessment design, and has authored the Practice NCEA Assessments included in the Pearson Teaching Resources.