Concepts of population, sample, random sample, discrete and continuous data. Reliability of data sources and bias in sampling. Interpretation of outliers. Sampling techniques and their effectiveness.

Presentation of data (discrete and continuous): frequency distributions (tables). Histograms. Cumulative frequency; cumulative frequency graphs; use to find median, quartiles, percentiles, range and interquartile range (IQR). Production and understanding of box and whisker diagrams.

Measures of central tendency (mean, median and mode). Estimation of mean from grouped data. Modal class. Measures of dispersion (interquartile range, standard deviation and variance). Effect of constant changes on the original data. Quartiles of discrete data.

Linear correlation of bivariate data. Pearson’s product-moment correlation coefficient, r. hand Scatter diagrams; lines of best fit, by eye, passing through the mean point. Equation of the regression line of y on x. Use of the equation of the regression line for prediction purposes. Interpret the meaning of the parameters, a and b, in • a linear regression y = ax + b.

Concepts of trial, outcome, equally likely outcomes, relative frequency, sample space (U ) and event. The probability of an event A is P(A) = The complementary events A and A′ (not A). Expected number of occurrences.

Use of Venn diagrams, tree diagrams, sample space diagrams and tables of outcomes to calculate probabilities. Combined events: P(A ∪ B) = P(A) + P(B) … P(A ∩ B). Mutually exclusive events: P (A ∩ B) = 0. Conditional probability: P(A | B) = Independent events: P(A ∩ B) = P(A)P(B).

Concept of discrete random variables and their probability distributions. Expected value (mean), E X for discrete data. Applications.

Binomial distribution. Mean and variance of the binomial distribution.

The normal distribution and curve. Properties of the normal distribution. Diagrammatic representation. Normal probability calculations. Inverse normal calculations

Spearman’s rank correlation coefficient, rs. Awareness of the appropriateness and limitations of Pearson’s product moment correlation coefficient and Spearman’s rank correlation coefficient, and the effect of outliers on each.

Formulation of null and alternative hypotheses, H and H . 0 1 Significance levels. p -values. Expected and observed frequencies. The χ test for independence: contingency tables, degrees of freedom, critical value. The χ 2 goodness of fit test. The t -test. Use of the p -value to compare the means of two populations. Using one-tailed and two-tailed tests.

Design of valid data collection methods, such as surveys and questionnaires. Selecting relevant variables from many variables. Choosing relevant and appropriate data to analyse. Categorizing numerical data in a χ 2 table and justifying the choice of categorisation. Choosing an appropriate number of degrees of freedom when estimating parameters from data when carrying out the χ 2 goodness of fit test. Definition of reliability and validity. Reliability tests. Validity tests.

Non-linear regression. Evaluation of least squares regression curves using technology. Sum of square residuals (SSres) as a measure of fit for a model. The coefficient of determination (R2). Evaluation of R2 using technology.

Linear transformation of a single random variable. Expected value of linear combinations of n random variables. Variance of linear combinations of n independent random variables. x̄ as an unbiased estimate of μ. sn2 … 1 as an unbiased estimate of σ 2.

A linear combination of n independent normal random variables is normally distributed. particular, X~N μ, σ 2 ⇒ X̄~N μ, Central limit theorem.

Confidence intervals for the mean of a normal population.

Poisson distribution, its mean and variance. Sum of two independent Poisson distributions has a Poisson distribution.

Critical values and critical regions. Test for population mean for normal distribution. Test for proportion using binomial distribution. Test for population mean using Poisson distribution. Use of technology to test the hypothesis that the population product moment correlation coefficient ( ρ) is 0 for bivariate normal distributions. Type I and II errors including calculations of their probabilities.

Transition matrices. Powers of transition matrices. Regular Markov chains. Initial state probability matrices. Calculation of steady state and long-term probabilities by repeated multiplication of the transition matrix or by solving a system of linear equations.