About the Book
This revised and updated edition has been specifically designed to comprehensively and expertly address the key skills and knowledge areas set out in the 2000 edition of the Mathematics Study Design. It emphasises relevant applications with clear examples and excellent exercises which specifically include questions and examples that foster effective and appropriate use of technology. Also included are excellent revision summaries and exercises, as well as analysis questions in every chapter to ensure that students are thoroughly prepared for examinations. Answers are provided for all exercises. Fully worked solutions to all applications and analysis questions are provided in Essential Further Mathematics Solutions Supplement (second edition).
Table of Contents:
Acknowledgments; Introduction; Core: 1. Types of data and frequency tables, 1.1. Some data, 1.2. Variables, 1.3. Types of data - numerical and categorical, 1.4. Looking at distributions, 1.5. Grouping data, 1.6. Percentage frequencies, 1.7. Cumulative frequencies, 1.8. Chapter outcomes, 2. Picturing data - histograms, stem plots and barcharts, 2.1. The histogram, 2.2. What to look for in a histogram, 2.3. The stem-and-leaf plot, 2.4. From stem plot to histogram, 2.5. The barchart, 2.6. Chapter outcomes, 3. Summarising numerical data - the median, range, IQR and box plots, 3.1. Will less than the whole picture do?, 3.2. The median, range and interquartile range (IQR), 3.3. The five-number summary and the box plot, 3.4. Box plots with outliers, 3.5. Relating a box plot to distribution shape, 3.6. Using box plots to compare distributions, 3.7. Chapter outcomes, 4. Summarising numerical data - the mean and the standard deviation, 4.1. The mean and the standard deviation, 4.2. The relationship between the mean and the median, 4.3. Measuring the spread around the mean, 4.4. The variance, 4.5. The standard deviation, 4.6. Estimating the standard deviation from range, 4.7. Calculating the mean and standard deviation using a statistical calculator, 4.8. Giving meaning to the standard deviation, 4.9. Chapter outcomes, 5. Populations and samples, 5.1. Populations, 5.2. Samples, 5.3. Simple random sample (SRS), 5.4. Other sampling methods, 5.5. Population parameters and sample statistics, 5.6. Chapter outcomes, 6. Displaying and describing relationships between numerical variables, 6.1. Displaying relationships - the scatterplot, 6.2. Characteristics of a relationship, 6.3. The correlation coefficient, 6.4. Some traps with Pearson's correlation coefficient r, 6.5. The coefficient of determination, 6.6. Dependent and independent variables, 6.7. Correlation and causality, 6.8. Chapter outcomes, 7. Displaying and describing relationships between categorical variables, 7.1. The two-way frequency table, 7.2. Reading a two-way frequency table, 7.3. Percentaging a two-way frequency table, 7.4. Using percentages to identify relationships, 7.5. Using a segmented barchart to identify relationships in tabulated data, 7.6. Dependent and independent variables in tabulated data, 7.7. Locating the dependent variable in a table, 7.8. Choosing the appropriate graphical display, 7.9. Investigating the relationship between a numerical and a categorical variable?, 7.10 Chapter outcomes, 8. Regression - fitting lines to data, 8.1. Introduction, 8.2. Least squares regression, 8.3. Performing a regression analysis, 8.4. A graphical approach to regression - the three median line, 8.5. Chapter outcomes, 9. Regression - residual plots and data transformation, 9.1. Testing the goodness of fit of a regression line, 9.2. What do we do when a residual plot shows evidence of non-linearity in our data?, 9.3. Putting all the parts together - regression analysis with data transformation, 9.4. Chapter outcomes, 10. Time series - finding the pattern, 10.1. Definition of time series, 10.2. Characteristics of a time series plot, 10.3. Interpreting a time series plot, 10.4. Smoothing, 10.5. Seasonal indices, 10.6. Fitting a trend line, 10.7. Forecasting, 10.8. Chapter outcomes, 11. Revision of the core - summary and multiple choice questions, 11.1. Chapter by chapter revision of the core, 11.2. Displaying, summarising and describing univariate data, 11.3. Displaying, summarising and describing bivariate data, 11.4. Regression, 11.5. Time series; Module 1. Number patterns and applications: 12. Ratio and proportion, 12.1. Introduction, 12.2. Expressing ratios in their simplest form, 12.3. Expressing ratios as fractions or percentages of the whole, 12.4. Dividing quantities in given ratios, 12.5. Ratio and proportion, 12.6. Applications of ratio and proportion, 13. Arithm
