What you’ll learn12 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, lines of best fit and Pearson correlation coefficient r.• Distinguish positive/negative/zero and strong/weak/no correlation.• Correlation does not imply causation; use regression line for prediction with caution.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 P(A union B)=P(A)+P(B)-P(A intersection B).• Use conditional probability and independence, with/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—Regression x on y• Use equation of regression line of x on y for prediction.• Know prediction direction matters; an x-on-y line is not always reliable for predicting y from x.Syllabus objective—SL 4.11—Formal conditional probability• Use P(A|B)=P(A intersection B)/P(B).• Use P(A intersection B)=P(B)P(A|B).• Test for independence using conditional probability.Syllabus objective—SL 4.12—Standardizing normal variables• Standardize normal variables using z-values.• z-value measures number of standard deviations from the mean.• Use z-values to find unknown means and standard deviations.Syllabus objective