Probability
Venn diagrams and tables
Set notation
Two-step sample spaces
Experimental probability
Measures of centre
Stem-and-leaf plots
Grouped data and histograms
Measures of spread
Box plots
Surveys and statistical investigations
Place a probability on the 0–1 chance scale, name its qualitative band and order probability expressions written in different equivalent forms by value Distinguish a random experiment, one outcome, the full sample space and an event as a subset of that sample space Construct or recognise a complete finite sample space, preserving order where successive stages make ordered tuples distinct For equiprobable outcomes, calculate an event probability as favourable outcomes divided by all outcomes and verify that it lies from zero to one Obtain the probability of the complement as one minus the event probability and interpret impossible and certain boundary cases Convert a fraction to a percentage Convert a decimal to a percentage Convert a percentage to a fraction Convert a percentage to a decimal Simplify a fraction Form or recognise the union, intersection, difference and complement of finite or interval-defined sets relative to an explicitly stated universe Decimal place value Read, complete and translate a two-set Venn diagram of counts: identify the only, total, union, intersection, complement and neither regions, convert between a Venn diagram and a two-way table, and state the probability of a named region from the total Interpret unions, intersections and complements as “at least one”, “both”, “only”, “neither” and related event descriptions relative to a stated sample space Complete and read a two-event count or probability table, including four interior regions, row and column margins and the grand total Calculate a union by adding the marginal probabilities and subtracting the intersection once Determine whether events can occur together and use the zero-intersection special case of the addition rule without confusing exclusivity with independence Construct and read a two-way frequency table from paired categorical records Distinguish an element statement from a subset statement and decide whether a finite set is contained in another stated set Signed numbers Represent a two- or three-stage finite experiment by an ordered list, grid, table or tree and count its elementary outcomes without collapsing ordered outcomes Calculate an experimental probability as a relative frequency from given or collected count data, reduce it exactly, and interpret a relative frequency as an estimate of probability Calculate an expected number of occurrences as probability multiplied by the number of trials, and use relative frequencies to estimate an unknown composition or count at a different group size Multiplication and division Choose a random device, outcome mapping, replacement rule, repetition unit and success condition that simulate the stated experiment without changing its probabilities Calculate an estimated probability as the exact success count over trial count and interpret repeated-run variation without claiming that a finite simulation equals the theoretical probability Identify the mode(s) of a small numerical data list, including bimodal and no-unique-mode cases, and distinguish the modal value from its frequency Calculate the mean Calculate the median Identify a clear outlier relative to the body of a data set and calculate or describe its effect on the mean and median when the outlier is included or removed Choose the appropriate measure of centre Order data and locate a value by position Build a frequency table for discrete numerical data Identify the mode of a categorical distribution Construct or read a stem plot Read a back-to-back stem plot Classify distribution shape Compare distributions across groups Construct or read a histogram Build a grouped frequency table Choose class intervals for grouped data Calculate percentage frequency Read a value from a frequency table or bar chart Construct or read a bar chart Calculate the quartiles Calculate the interquartile range Calculate the range Choose the appropriate measure of spread Produce a five-number summary Construct or read a boxplot Read percentages from a boxplot Classify a described collection as a population, a sample or a census, and identify the population for a stated survey Evaluate a survey question for clarity, neutrality and answer-format match, identifying ambiguous, leading, double-barrelled or overlapping-option questions and checking attitude option lists for an odd number of options with a neutral midpoint Evaluate whether a described sampling method is likely to give a representative sample, identifying convenience sampling, self-selection, under-coverage and samples too small for the claimed conclusion Link a statistical claim in a short described report or display to the summary statistic or display feature that supports or contradicts it, and identify misleading presentation Classify a variable as categorical or numerical Choose a display to suit the data