4. Statistics & Probability

Course Description
This course introduces students to the core concepts and techniques of statistics and probability within the IBDP Analysis & Approaches framework. SL students learn to collect, summarize, display, and interpret data; calculate measures of central tendency and dispersion; model discrete and continuous random processes; and apply probability rules. HL students deepen this knowledge with Bayes’ theorem and advanced properties of random variables—preparing them for further study in data science, economics, and the social sciences.

Learning Outcomes

SL Students will be able to:

• Explain the concepts of reliability, bias, and common sampling techniques.
• Construct and interpret histograms, cumulative‐frequency graphs, and box‐and‐whisker plots.
• Calculate mean, median, mode, mid‐interval mean, variance, and standard deviation for ungrouped and grouped data.
• Determine quartiles, interquartile range, and identify outliers.
• Draw scatter diagrams, compute Pearson’s correlation coefficient \(r\), and find the regression line of $y$ on $x$.
• Define probability concepts, including expected value of a random variable.
• Use Venn diagrams to solve problems involving combined, mutually exclusive, and conditional probabilities, and test for independence.
• Work with discrete random variables: compute probability mass functions and expectations.
• Apply the binomial distribution to model repeated independent binary trials.
• Use the normal distribution to approximate probabilities and calculate areas via $z$‐scores.
• Perform linear regression analysis, interpreting slope and intercept in context.
• Solve conditional‐probability problems and test events for independence.
• Use the inverse normal function to determine unknown means and standard deviations.

HL Students will additionally be able to:

• Use the inverse normal function to determine unknown means and standard deviations.
• Apply Bayes’ theorem to update probabilities in light of new evidence.
• Explore further properties of discrete and continuous random variables, including moment‐generating functions and transformations.