Mathematics: Analysis and Approaches SL

Statistics and probability

Descriptive statistics, probability, random variables, binomial and normal models, correlation, regression, and technology interpretation.

Calculate descriptive statistics Calculate and interpret mean, median, and range from small data sets with clear statistical reasoning. Interpret box plots and cumulative frequency Interpret quartiles, interquartile range, outlier boundaries, and distribution summaries. Use correlation and regression Use correlation and regression lines to interpret association and make sensible predictions. Calculate probability with diagrams Calculate probability from sample spaces and simple diagrams with exact fractions. Use conditional probability Calculate and interpret conditional probability from two-way information. Use binomial distributions Model repeated independent trials with binomial probabilities. Use normal distributions Standardize normal-distribution values and interpret z-scores. Read values from a bar chart Read the height of a named bar directly off a bar chart on a value grid. Builds the data-handling skill of extracting a value from a categorical chart, not being given it in the text. Find a difference from a bar chart Read the heights of two bars off a bar chart and find the difference. Extends bar-chart reading into "read then compute" by comparing two categories. Predict from a line of best fit Use the line of best fit on a scatter graph to predict a y-value at a given x. Reads the trend line, not an individual data point - a core skill for correlation and regression. Read a value from a pie chart Read a sector angle off a pie chart and calculate the number in that category as (angle / 360) times the total. Combines chart reading with proportion. Evaluate samples and statistical evidence Evaluate sampling, missing data, cumulative distributions, and comparisons without confusing a sample statistic with a population claim. Read a frequency from a histogram Read the frequency of a class interval off a histogram. Reinforces that a histogram has touching bars over a continuous scale, unlike a bar chart of categories. Analyse grouped and transformed data Use grouped-data estimates, population variance, standard deviation, and forward or reverse constant changes to complete data sets. Estimate the median from a cumulative frequency curve Use a cumulative frequency curve (ogive) to estimate the median or quartiles: read across from the cumulative frequency axis to the curve, then down to the data axis. Analyse correlation and regression Use Pearson correlation, GDC regression, interpolation, extrapolation, and the correct x-on-y regression model. Read values from a box-and-whisker plot Read the five-number summary (minimum, quartiles, median, maximum) off a box-and-whisker plot, and find the interquartile range and range. Model combined probability and expectation Use Venn diagrams, trees, tables, discrete random variables, expected value, fair games, and formal independence tests. Use binomial and normal models Use GDC binomial and normal calculations, model checks, inverse probabilities, and z-score equations with unknown parameters.