What you’ll learn11 learning objectivesChoose one objective for a focused lesson, or study the complete topic.—SL 4.1—Sampling and data• 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.Syllabus objective—SL 4.2—Data presentation• Use frequency tables, histograms and cumulative frequency graphs.• Find median, quartiles, percentiles, range and IQR.• Produce and compare box-and-whisker diagrams; mark outliers.Syllabus objective—SL 4.3—Summary statistics• 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.Syllabus objective—SL 4.4—Correlation and regression• 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.Syllabus objective—SL 4.5—Probability basics• 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.Syllabus objective—SL 4.6—Combined, conditional and independent events• Use Venn, tree, sample-space diagrams and outcome tables.• Use combined-event, conditional-probability and independence formulae.• Handle probabilities with and without replacement.Syllabus objective—SL 4.7—Discrete random variables• Understand discrete random variables and probability distributions.• Find expected value/mean; interpret E(X)=0 as a fair game context.Syllabus objective—SL 4.8—Binomial distribution• Use binomial distribution as an appropriate model.• Use mean and variance of binomial distribution.• Use technology for binomial probabilities; formal proofs are not required.Syllabus objective—SL 4.9—Normal distribution• 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.Syllabus objective—SL 4.10—Spearman's rank correlation• Use Spearman's rank correlation coefficient rs with technology.• Average ranks for tied data.• Compare Pearson vs Spearman, including monotonic relationships and outlier sensitivity.Syllabus objective—SL 4.11—Hypothesis testing• 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.Syllabus objective
