Year 12: Statistical Analysis

6 dot points across 6 inquiry questions, in syllabus order. Each dot point has a focused answer, with exam-style questions and worked answers where available.

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

Normal distribution. The bell-shaped curve, the empirical $68$ - $95$ - $99.7$ rule built band by band, mean and standard deviation as the two parameters, how the questions are worded, and worked Australian examples for heights, exam marks and manufacturing quality control.

12 min read →

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

Interpolation vs extrapolation. The data range as the dividing line, why predictions inside are reliable and outside are suspect, a stage-by-stage diagram of the zones, how the questions are worded, and Australian-context worked examples.

10 min read →

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

Scatterplots. Reading form, direction and strength of association, identifying outliers, correlation versus causation, a stage-by-stage construction, and worked Australian examples using study, climate and household data.

12 min read →

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

Z-scores. The formula $z = (x - \mu)/\sigma$ , standardising a value step by step, interpreting z-scores as standard-deviation distances, comparing observations from different normal distributions, reversing to find a value from a percentile, and worked Australian examples from exam marks and salary data.

12 min read →

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

Least-squares regression line. The equation $y = mx + b$ , finding the gradient and intercept on a calculator, predicting and reading values off the line, interpreting the gradient and intercept, interpolation versus extrapolation, and worked Australian examples.

13 min read →

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

Pearson's correlation coefficient. What $r$ measures, how to read its sign and magnitude, the strength scale, the non-linear limitation, computing it on a calculator, and worked Australian examples.

11 min read →