Table of Contents

About eBookPLUS vii Topic 1 -- Univariate data 1 Exercise 1.2 -- Types of data 1 Exercise 1.3 -- Stem plots 1 Exercise 1.4 -- Dot plots, frequency tables and histograms, and bar charts 3 Exercise 1.5 -- Describing the shape of stem plots and histograms 6 Exercise 1.6 -- The median, the interquartile range, the range and the mode 8 Exercise 1.7 -- Boxplots 11 Exercise 1.8 -- The mean of a sample 14 Exercise 1.9 -- Standard deviation of a sample 17 Exercise 1.10 -- Populations and simple random samples 17 Exercise 1.11 -- The 68-95-99.7% rule and z-scores 18 Topic 2 -- Comparing data sets 23 Exercise 2.2 -- Back-to-back stem plots 23 Exercise 2.3 -- Parallel boxplots and dot plots 26 Exercise 2.4 -- Two-way (contingency) frequency tables and segmented bar charts 28 Topic 3 -- Introduction to regression 33 Exercise 3.2 -- Response (dependent) and explanatory (independent) variables 33 Exercise 3.3 -- Scatterplots 33 Exercise 3.4 -- Pearson's product-moment correlation coefficient 35 Exercise 3.5 -- Calculating r and the coefficient of determination 36 Exercise 3.6 -- Fitting a straight line -- least-squares regression 38 Exercise 3.7 -- Interpretation, interpolation and extrapolation 40 Exercise 3.8 -- Residual analysis 43 Exercise 3.9 -- Transforming to linearity 46 Topic 4 -- Time series 51 Exercise 4.2 -- Time series and trend lines 51 Exercise 4.3 -- Fitting trend lines and forecasting 53 Exercise 4.4 -- Smoothing time series 58 Exercise 4.5 -- Smoothing with an even number of points 63 Exercise 4.6 -- Median smoothing from a graph 67 Exercise 4.7 -- Seasonal adjustment 69 Topic 5 -- Recurrence relations 77 Exercise 5.2 -- Generating the terms of a first-order recurrence relation 77 Exercise 5.3 -- First-order linear recurrence relations 79 Exercise 5.4 -- Graphs of first-order recurrence relations 82 Topic 6 -- Interest and depreciation 87 Exercise 6.2 -- Simple interest 87 Exercise 6.3 -- Compound interest tables 90 Exercise 6.4 -- Compound interest formula 92 Exercise 6.5 -- Finding rate or time for compound interest 96 Exercise 6.6 -- Flat rate depreciation 100 Exercise 6.7 -- Reducing balance depreciation 103 Exercise 6.8 -- Unit cost depreciation 106 Topic 7 -- Loans, investments and asset value 111 Exercise 7.2 -- Reducing balance loans I 111 Exercise 7.3 -- Reducing balance loans II 115 Exercise 7.4 -- Reducing balance loans III 118 Exercise 7.5 -- Reducing balance and flat rate loan comparisons 125 Exercise 7.6 -- Effective annual interest rate 127 Exercise 7.7 -- Perpetuities 129 Exercise 7.8 -- Annuity investments 132 Topic 8 -- Matrices 137 Exercise 8.2 -- Matrix representation 137 Exercise 8.3 -- Addition, subtraction and scalar operations with matrices 138 Exercise 8.4 -- Multiplying matrices 141 Exercise 8.5 -- Multiplicative inverse and solving matrix equations 147 Exercise 8.6 -- Dominance and communication matrices 149 Exercise 8.7 -- Application of matrices to simultaneous equations 151 Exercise 8.8 -- Transition matrices 153 Topic 9 -- Undirected graphs and networks 159 Exercise 9.2 -- Basic concepts of a network 159 Exercise 9.3 -- Planar graphs and Euler's formula 161 Exercise 9.4 -- Walks, trails, paths, cycles and circuits 162 Exercise 9.5 -- Trees and their applications 164 Topic 10 -- Directed graphs and networks 169 Exercise 10.2 -- Critical path analysis 169 Exercise 10.3 -- Critical path analysis with backward scanning and crashing 173 Exercise 10.4 -- Network flow 180 Exercise 10.5 -- Assignment problems and bipartite graphs 184 Topic 11 -- Geometry: similarity and mensuration 191 Exercise 11.2 -- Properties of angles, triangles and polygons 191 Exercise 11.3 -- Area and perimeter I 193 Exercise 11.4 -- Area and perimeter II 196 Exercise 11.5 -- Great circles 198 Exercise 11.6 -- Total surface area 200 Exercise 11.7 -- Volume of prisms, pyramids and spheres 203 Exercise 11.8 -- Similar figures 207 Exercise 11.9 -- Similar triangles 208 Exercise 11.10 -- Triangulation -- similarity 212 Exercise 11.11 -- Area and volume scale factors 215 Exercise 11.12 -- Time zones 221 Topic 12 -- Trigonometry 223 Exercise 12.2 -- Trigonometry 223 Exercise 12.3 -- Pythagorean triads 225 Exercise 12.4 -- Three-dimensional Pythagoras' theorem 227 Exercise 12.5 -- Trigonometric ratios 229 Exercise 12.6 -- The sine rule 232 Exercise 12.7 -- Ambiguous case of the sine rule 235 Exercise 12.8 -- The cosine rule 237 Exercise 12.9 -- Special triangles 239 Exercise 12.10 -- Area of triangles 241 Topic 13 -- Applications of geometry and trigonometry 245 Exercise 13.2 -- Angles 245 Exercise 13.3 -- Angles of elevation and depression 247 Exercise 13.4 -- Bearings 250 Exercise 13.5 -- Navigation and specification of locations 254 Exercise 13.6 -- Triangulation -- cosine and sine rules 259 Topic 14 -- Construction and interpretation of graphs 267 Exercise 14.2 -- Constructing and interpreting straight-line graphs 267 Exercise 14.3 -- Line segments and step functions 273 Exercise 14.4 -- Simultaneous equations and break-even point 278 Exercise 14.5 -- Interpreting non-linear graphs 282 Exercise 14.6 -- Constructing non-linear relations and graphs 285 Topic 15 -- Linear inequalities and linear programming 291 Exercise 15.2 -- Linear inequalities 291 Exercise 15.3 -- Simultaneous linear inequalities 293 Exercise 15.4 -- Linear programming 298 Exercise 15.5 -- Applications 304