Stage 5, Statistics & Probability

Module 4 – Statistics & Probability

This module equips students with tools to collect, represent, and interpret data, while also exploring the mathematics of chance. It blends practical data analysis with theoretical probability, preparing learners for advanced pathways and real‑world applications.

1. Bivariate Data: Scatter Plots, Correlation & Line of Best Fit

• Scatter plots: Students plot two variables to visually explore relationships (e.g., height vs. weight).

• Correlation: Understanding positive, negative, and zero correlation.

• Line of best fit: Drawing or calculating a trend line to model the relationship.

• Applications: Predicting outcomes (e.g., sales vs. advertising spend), identifying patterns in science experiments.

2. Probability Distributions (Binomial & Conditional Probability – Stage 5.3)

• Binomial distribution: Modelling repeated independent trials with two outcomes (success/failure).

  • Example: probability of getting exactly 3 heads in 5 coin tosses.

• Conditional probability: Calculating probabilities when one event affects another.

  • Example: probability of drawing a red card given that the card is a face card.

• Applications: Risk analysis, genetics, quality control, and decision‑making under uncertainty.

3. Independent & Dependent Events

• Independent events: Outcomes that do not affect each other (e.g., rolling two dice).

• Dependent events: Outcomes where one influences the other (e.g., drawing cards without replacement).

• Students learn to calculate probabilities using multiplication and addition rules.

• Applications: games of chance, probability in everyday scenarios, and statistical modelling.

4. Advanced Data Analysis: Regression & Trend Lines (Stage 5.3)

• Regression analysis: Using statistical methods to quantify relationships between variables.

• Trend lines: Extending beyond simple lines of best fit to more complex models.

• Technology integration: Using calculators or software to compute regression equations and correlation coefficients.

• Applications: economics, business forecasting, scientific research.

5. Using Technology for Statistical Analysis

• Students use graphing calculators, spreadsheets, or statistical software to:

  • Plot data sets.

  • Calculate correlation coefficients.

  • Generate regression equations.

  • Simulate probability experiments.

• This builds digital literacy and prepares students for data‑driven fields.

Learning Outcome

By the end of Module 4, students will:

• Represent and interpret bivariate data with scatter plots and lines of best fit.

• Understand and apply probability distributions, including binomial and conditional cases.

• Distinguish between independent and dependent events and calculate their probabilities.

• Use regression and trend lines for advanced data analysis.

• Confidently apply technology to explore and solve statistical problems.