Sigma Statistics is a brand-new statistics-focussed textbook following in the tradition of Sigma Mathematics.
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.
The parts of the course that have evolved from the current NCEA Level 3 Statistics and Modelling Achievement Standards have been extensively upgraded. The content has been carefully revised in line with best teaching practice, and expanded to respond to changes in the curriculum and assessment. Among the mathematical changes are:
new material on probability distributions (Achievement Standard 3.14), focussing on mean and standard deviation being properties of a distribution
coverage of deterministic vs. probabilistic concepts, or true vs. experimental vs. theoretical probability (Achievement Standard 3.13)
new material on risk and relative risk that strengthens the probability section in Achievement Standard 3.13
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
CAS calculator applications
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
25 Combining distributions and random variables
Appendix 1: Using the Central Limit Theorem to construct confidence intervals
Appendix 2: Statistical and mathematical proofs
Appendix 3: Formulae
Appendix 4: Statistical tables
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.
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