4.1 Statistics and probability - SL content

• Understand population, sample, random sample, discrete and continuous data.

• Assess reliability, bias, missing data, recording errors and outliers.

• Use simple random, convenience, systematic, quota and stratified sampling.

• Use frequency tables, histograms and cumulative frequency graphs.

• Find median, quartiles, percentiles, range and IQR.

• Produce and compare box-and-whisker diagrams; mark outliers.

• Use mean, median, mode, modal class and grouped-data mean estimates.

• Use IQR, standard deviation and variance; technology may calculate SD/variance.

• Understand effects of adding/subtracting or scaling all data values.

• Use scatter diagrams, best-fit lines and Pearson correlation coefficient r.

• Distinguish correlation strength/direction and correlation vs causation.

• Use y-on-x regression for prediction; interpret parameters and beware extrapolation.

• Use trial, outcome, sample space, event and relative frequency.

• Calculate P(A)=n(A)/n(U), complements and expected number of occurrences.

• Represent sample spaces with lists or tables.

• Use Venn, tree, sample-space diagrams and outcome tables.

• Use combined-event, conditional-probability and independence formulae.

• Handle probabilities with and without replacement.

• Understand discrete random variables and probability distributions.

• Find expected value/mean; interpret E(X)=0 as a fair game context.

• Use binomial distribution as an appropriate model.

• Use mean and variance of binomial distribution.

• Use technology for binomial probabilities; formal proofs are not required.

• Use normal distribution curve and its properties.

• Use 68-95-99.7 rule around mean and standard deviation.

• Use technology for normal and inverse-normal probabilities.

• Use Spearman's rank correlation coefficient rs with technology.

• Average ranks for tied data.

• Compare Pearson vs Spearman, including monotonic relationships and outlier sensitivity.

• Form null/alternative hypotheses, significance levels and p-values.

• Use chi-square tests for independence and goodness of fit.

• Use t-tests for comparing two population means; interpret test results.

• At SL, t-test samples are unpaired and population variance is unknown.