Unit Overview
Statistics and Probability
IB Mathematics AI SLΒ· 5 min read π 24-26% of overall exam
1. Unit at a Glance
This unit follows a clear logical learning arc: we start with foundational data classification, move to visualising and summarising data, explore relationships between variables, build up core probability rules, and end with the two most common probability distributions tested at AI SL.
Nearly all questions in this unit are context-based, and many require interpreting output from your GDC, so building confidence with technological tools for statistical calculations is a key theme throughout your learning.
This unit is split into 10 focused sub-topics to learn step-by-step:
Discrete and continuous data types
Learn the core classification of data types, the foundation for all subsequent statistical analysis.
β β± 4 min
Data representation: histograms, box plots, cumulative frequency
Create and interpret common data visualisations for both discrete and continuous data sets.
β β β± 6 min
Measures of central tendency
Calculate and compare mean, median and mode for ungrouped and grouped data.
β β± 5 min
Measures of spread: variance, standard deviation
Quantify spread in data using range, interquartile range, variance and standard deviation.
β β β± 5 min
Correlation and linear regression
Measure linear correlation between two variables and fit regression lines for prediction.
β β β β± 7 min
Basic probability concepts and combined events
Learn core probability rules and solve problems for combined events using Venn diagrams.
β β β± 6 min
Conditional probability and independence
Calculate conditional probability and test for independence of two events.
β β β β± 5 min
Discrete probability distributions
Understand properties of discrete distributions and calculate expected value.
β β β β± 5 min
Binomial distribution
Identify binomial conditions and calculate probabilities, expectation and variance.
β β β β± 6 min
Normal distribution and applications
Apply the normal distribution to calculate probabilities and inverse values for real problems.
β β β β β± 7 min
2. Common Pitfalls
Wrong move:
Confusing discrete and continuous data when choosing the correct graph or calculation method.
Why:
Exam questions often penalise incorrect classification leading to wrong approaches.
Correct move:
Always check if data can only take specific values (discrete) or any value in a range (continuous) first.
Wrong move:
Using sample standard deviation instead of population standard deviation for GDC calculations.
Why:
AI SL questions almost always require population standard deviation unless explicitly stated otherwise.
Correct move:
Confirm which standard deviation value your question asks for before reporting your answer.
Wrong move:
Applying the binomial distribution without checking its required conditions.
Why:
You will lose method marks for not verifying the model is appropriate for the problem.
Correct move:
Always check for fixed trials, two outcomes, independent trials and constant probability before using binomial.
3. Quick Reference Cheatsheet
Concept / Formula | Description |
|---|---|
Mean (ungrouped data) | |
Mean (grouped data) | |
Pearson's | Measures strength of linear correlation between and |
Combined events probability | |
Conditional probability | |
Binomial expectation | |
Binomial variance | |
Normal distribution notation | where = mean, = variance |
What's Next
Start your learning of this unit with the first sub-topic, which introduces core data classification that all later statistical work builds on. Once you complete all 10 sub-topics in this unit, you will move on to the next unit covering core calculus concepts for applications.