4 Statistics and probability

• 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, 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.

• 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 P(A union B)=P(A)+P(B)-P(A intersection B). • Use conditional probability and independence, with/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 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.

• 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.

• 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.

AHL 4.13 (HL)—Bayes' theorem

• Use Bayes' theorem for up to three events. • Connect to conditional probability and independent events.

AHL 4.14 (HL)—Random variables and probability density

• Use variance of a discrete random variable. • Use continuous random variables and probability density functions, including piecewise functions. • Find mode, median, mean, variance and standard deviation for random variables. • Use E(X), E(X^2), Var(X)=E(X^2)-[E(X)]^2 and linear transformations.