Sigma Statistics eBook: Digital Access Code - 1 year lease: NCEA Level 3

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About the book

Sigma Statistics is a 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.

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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 Statistical interference - making comparisons
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 needs no introduction to a generation of New Zealand mathematics students and teachers. He has written a full six-book, award-winning series for secondary-school mathematics, and his material has also been published in Australia, South Africa, Fiji and Abu Dhabi. David Barton was educated at Wellington College and has taught at Wellington College and Rangitoto College in Auckland.

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Please note: eBooks are available for download immediately and cannot be returned once purchased.

Find out more about Barton Mathematics.

Visit David Barton's website for additional links for each text, spreadsheets, statistics resources and more.

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