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