This module will expose students to fundamental statistical techniques, and develop analytical problem solving skills.
Basic mathematics
Mathematical notation: Sigma notation and subscripts. Rounding & accuracy. Equation of a line and understanding of slope. Use of a calculator. Absolute and relative error. Percentages. Calculation order (BOMDAS). Basic manipulation of equations (reverse BOMDAS).
Data Collection & Presentation
Sampling techniques & Bias. Basic sample size. Collection & classification of data. Primary and secondary data. Continuous and discrete data. Graphical and tabular representation of data. Histograms, polygons and curves. Simple and grouped frequency distributions. Class boundaries, widths, mid-points, scaling factors, scaled frequency, cumulative frequencies, percentage frequencies. Cumulative and percentage frequency distributions. Non-numeric frequency distributions and charts.
Data Analysis
Averages, mean, median and mode of grouped and ungrouped data. Diagrammatic and formulaic determination of the median and other quantiles, and the mode. Measures of dispersion, standard deviation, range, inter-quartile range, coefficient of variation. Concept of skewness.
Regression Techniques
Method of least squares for time series and other data. Linear relationship modelling. Moving averages for time series. Time series trend & adjusted seasonal components. Additive and multiplicative time series models. Deseasonalised data. Correlation. Scatter diagrams. Strong, weak, positive, negative and spurious correlation. Rank correlation.
Basic Probability
Basic understanding of probability as a proportion. Contingency tables and Venn diagrams. Conditional and unconditional probability. Mutually exclusive, complementary, independent and dependent events. General and basic addition rules and multiplication rules. Application of probability to reliability and systems. Permutations and combinations. Bayes’ Theorem, and Bayesian statistics. Contingency tables and decision trees. Expected value. Expected versus most likely values.
Probability Distributions
Introduction to random variables and probability distributions for them. Discrete and continuous variables. Expected value. Binomial distribution. Poisson distribution. Uniform distribution. Normal distribution, and standard normal tables. Inverse normal problems, confidence intervals and control charts. t-distribution for "small" sample sizes, and corresponding confidence intervals. Central limit theorem. t-Test for a single mean: Correct interpretation of p values in terms of evidence, sample size, and power.
| Module Content & Assessment | |
|---|---|
| Assessment Breakdown | % |
| Other Assessment(s) | 100 |