Applications and Interpretation SL
 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
 Model 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 productmoment correlation coefficient, r
 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) = n(A) / n(U)
 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 and mutually exclusive events
 Conditional probability
 Independent events
 Concept of discrete random variables and their probability distributions
 Expected value (mean), E(X) for discrete data
 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, r_{s}
 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_{0} and H_{1}
 Significance levels
 p values
 Expected and observed frequencies
 The χ^{2} 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 onetailed and twotailed tests

Analysis and Approaches SL
 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
 Model 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 productmoment correlation coefficient, r
 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) = n(A) / n(U)
 The complementary events A and A′ (not A)
 Use of Venn diagrams, tree diagrams, sample space diagrams and tables of outcomes to calculate probabilities
 Combined events and mutually exclusive events
 Conditional probability
 Independent events
 Concept of discrete random variables and their probability distributions
 Expected value (mean), 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
 Equation of the regression line of x on y
 Use of the equation for prediction purposes
 Use of the probability formulae for conditional and independent events
 Standardization of normal variables (z– values)
 Inverse normal calculations where mean and standard deviation are unknown
