Unit Overview

Statistics & Probability

IB Mathematics: Analysis and Approaches SL· 6 min read 📊 15-18% of overall IB AA SL examination

1. Unit at a Glance

This unit progresses logically from foundational descriptive statistics to applied probability modelling. We start with how data is collected and classified, then cover how to represent and summarize data numerically, before moving into core probability rules and finally modelling random processes with the two key distributions required for SL.

All sub-topics build directly on prior content in this unit: understanding data types is required to select correct graphs and summary measures, while core probability fundamentals underpin all work on discrete and continuous probability distributions.

This unit is split into 8 core sub-topics:

Data types, sampling and bias

Learn to classify data types and evaluate sampling methods for common sources of bias.

★⏱ 8 min

Data representation: histograms, box plots, cumulative frequency

Master constructing and interpreting common statistical graphs for grouped and ungrouped data.

★★⏱ 10 min

Measures of central tendency and dispersion

Calculate and compare mean, median, mode, variance, standard deviation and interquartile range.

★★⏱ 12 min

Cumulative distributions and percentiles

Use cumulative frequency graphs to find percentiles, quartiles and medians for any dataset.

★★★⏱ 10 min

Probability, conditional probability and independent events

Apply Venn diagrams, tree diagrams and probability rules to solve combined event problems.

★★★⏱ 15 min

Discrete probability distributions, expectation and variance

Calculate expectation, variance and probabilities for general discrete probability distributions.

★★★⏱ 12 min

Binomial probability distribution

Identify binomial conditions and calculate probabilities, mean and variance for binomial distributions.

★★★★⏱ 15 min

Normal probability distribution

Calculate probabilities and inverse normal values for continuous normally distributed data.

★★★★⏱ 18 min

2. Common Pitfalls

Wrong move:

Skipping data classification before selecting a graph or summary measure

Why:

Using methods for continuous data on discrete categorical data leads to incorrect interpretation

Correct move:

Always classify your data type first before choosing how to analyze or represent it

Wrong move:

Mixing up the denominator in conditional probability calculations

Why:

Dividing by P(A) instead of P(B) for $P (A ∣ B)$ leads to wrong results even with correct intersection values

Correct move:

Explicitly write the condition into the formula $P (A ∣ B) = \frac{P ( A \cap B )}{P ( B )}$ to avoid confusion

Wrong move:

Applying binomial or normal distributions without checking their conditions

Why:

Using the wrong distribution leads to incorrect results even if your calculation steps are correct

Correct move:

Always verify conditions (fixed trials for binomial, continuous symmetric data for normal) before proceeding

3. Quick Reference Cheatsheet

Concept / Formula	Key Note for IB SL
Sample Standard Deviation	$s = \frac{\sum ( x - x ˉ ) ^{2}}{n - 1}$ is used for sample data in IB
Conditional Probability	$P (A ∣ B) = \frac{P ( A \cap B )}{P ( B )}$ for $P (B) > 0$
Independent Events	$P (A \cap B) = P (A) \times P (B)$ and $P (A ∣ B) = P (A)$
Expectation of Discrete $X$	$E (X) = μ = \sum x \cdot P (X = x)$
Variance of Discrete $X$	$V a r (X) = σ^{2} = E (X^{2}) - [E (X)]^{2}$
Binomial Distribution	$X \sim B (n, p)$ , $E (X) = n p$ , $V a r (X) = n p (1 - p)$
Standardized Normal Value	$Z = \frac{X - μ}{σ}$ for $X \sim N (μ, σ^{2})$
Interquartile Range	$I QR = Q_{3} - Q_{1}$ , resistant to outlier values

What's Next

Begin this unit with the first sub-topic on data classification, sampling and bias, which establishes core vocabulary for all subsequent statistics work in this unit. After you complete all 8 sub-topics in this Statistics & Probability unit, you can progress to the first topic of the next unit on calculus for IB AA SL.