Mathematics: Applications and Interpretation SL

Statistics and probability

Applied statistics, probability models, regression, technology interpretation, and data-based reasoning for Mathematics AI SL.

Interpret correlation and regression models Use a fitted linear model to interpret slope, intercept, correlation direction, and predictions in applied AI SL contexts. Calculate descriptive statistics with technology Use and interpret mean, median, spread, and technology summary statistics. Interpret box plots and outliers Read quartiles, interquartile range, skew, and outliers from summary displays. Interpret correlation strength and direction Use scatter plots and correlation values to describe association. Calculate expected value for a discrete distribution Calculate and interpret expected value as the probability-weighted mean of a discrete distribution. Calculate probability with diagrams Use tree diagrams, Venn diagrams, and sample spaces to calculate probability. Estimate statistics from grouped data Use class midpoints and frequencies to estimate statistics from grouped continuous data. Use binomial distributions in context Model repeated independent trials and interpret binomial probabilities. Compare distributions using box plots Compare the centres and spreads of two distributions using medians and interquartile ranges from box plots. Use normal distributions in context Standardize values and interpret normal probabilities in applied settings. 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. Evaluate sampling methods and bias Recognize simple random, systematic, stratified, and convenience samples and explain selection bias. 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.