← Maths Standard 2 syllabus

NSWMaths Standard 2

Year 12: Statistical Analysis

6 dot points across 6 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

What does Pearson's correlation coefficient measure, and how is it interpreted?

Calculate and interpret Pearson's correlation coefficient using statistical technology, including the sign and magnitude
A focused answer to the HSC Maths Standard 2 dot point on Pearson's correlation coefficient. What $r$ measures, how to interpret its sign and magnitude, the limitations of $r$ in non-linear relationships, and how to compute it using calculator statistics functions.
7 min answer →

What is the difference between interpolation and extrapolation, and why is extrapolation less reliable?

Distinguish between interpolation and extrapolation when using a regression line, and assess the reliability of predictions
A focused answer to the HSC Maths Standard 2 dot point on interpolation vs extrapolation. The reliability of predictions inside and outside the data range, examples of when extrapolation breaks down, and Australian-context worked examples.
6 min answer →

How is the least-squares regression line calculated, and how is it used to model a linear relationship between two variables?

Find and use the equation of the least-squares regression line to model a linear relationship between two variables
A focused answer to the HSC Maths Standard 2 dot point on the least-squares regression line. The equation $y = mx + b$ , finding the gradient and intercept using calculator statistics functions, interpreting the gradient in context, and worked Australian examples.
7 min answer →

What is the normal distribution, and how does the empirical rule give the percentage of data within $1$ , $2$ and $3$ standard deviations?

Recognise the features of the normal distribution and apply the empirical $68$ - $95$ - $99.7$ rule
A focused answer to the HSC Maths Standard 2 dot point on the normal distribution. The bell-shaped curve, the empirical $68$ - $95$ - $99.7$ rule, mean and standard deviation as the two parameters, and worked Australian examples for heights, exam marks and manufacturing quality control.
7 min answer →

How do scatterplots reveal the form, direction and strength of the relationship between two variables?

Construct and interpret scatterplots to describe the relationship between two variables in bivariate data
A focused answer to the HSC Maths Standard 2 dot point on scatterplots. Reading form, direction and strength of association, identifying outliers, and worked Australian examples using ABS-style economic and demographic data.
7 min answer →

What is a z-score, and how is it used to compare observations from different normal distributions?

Calculate z-scores and use them to compare values from different normal distributions and find probabilities
A focused answer to the HSC Maths Standard 2 dot point on z-scores. The formula $z = (x - \mu)/\sigma$ , interpreting z-scores as standard-deviation distances, comparing observations from different normal distributions, and worked examples from exam scores and Australian salary data.
7 min answer →