← Maths Advanced syllabus

NSWMaths Advanced

Year 12: Statistical Analysis

4 dot points across 4 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do we describe and model the relationship between two numerical variables?

Construct scatter plots, calculate and interpret Pearson's correlation coefficient, and fit and use the least-squares regression line
A focused answer to the HSC Maths Advanced dot point on bivariate data. Scatter plots, the Pearson correlation coefficient, the least-squares regression line, prediction, and the limits of extrapolation, with worked examples and exam traps.
9 min answer →

How do probability density functions describe continuous random variables, and how do we extract probabilities and summary statistics from them?

Use probability density functions and cumulative distribution functions to find probabilities, medians, modes, means and variances of continuous random variables
A focused answer to the HSC Maths Advanced dot point on continuous random variables. Probability density functions, cumulative distribution functions, computing probabilities by integration, and finding mean, median, mode and variance, with worked examples.
10 min answer →

How do we describe a discrete random variable and summarise its distribution with mean and variance?

Define a discrete random variable by its probability distribution, and calculate the expected value, variance and standard deviation
A focused answer to the HSC Maths Advanced dot point on discrete random variables. Probability distributions, expected value, variance, standard deviation, and linear transformations of a discrete random variable, with worked examples.
9 min answer →

How do we use the normal distribution and z-scores to compute probabilities and compare observations?

Use the normal distribution, z-scores, the empirical rule and the standard normal table to find probabilities and percentiles
A focused answer to the HSC Maths Advanced dot point on the normal distribution. Standardising with z-scores, the 68-95-99.7 empirical rule, computing probabilities and inverse-normal percentiles, with worked examples and exam traps.
9 min answer →