Mathematics: Applications and Interpretation HL

Statistics, probability, and inference

Rank correlation, chi-square testing, confidence intervals, hypothesis tests, and Markov-style probability models.

Use Spearman rank correlation Rank paired data, calculate rank differences, and interpret Spearman correlation in context. Use chi-square tests for independence Calculate expected counts, chi-square contributions, degrees of freedom, and contextual conclusions. Construct confidence intervals Calculate margins of error and interval endpoints for means or proportions in applied contexts. Use hypothesis tests with normal and t models Standardise a test statistic, compare with a decision rule, and interpret the conclusion in context. Use Markov chains and steady states Interpret transition probabilities, next-state distributions, and two-state steady-state behaviour. 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. 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. 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. 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.