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.

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

Discrete random variables. Probability distributions, expected value, variance, standard deviation, and linear transformations of a discrete random variable, with worked examples.

14 min read →

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

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.

14 min read →

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

Normal distribution. Standardising with z-scores, the 68-95-99.7 empirical rule, computing probabilities as areas under the curve and inverse-normal percentiles, with worked examples and exam traps.

14 min read →

How do we display a single set of data and summarise its centre, spread and shape?

Display and summarise univariate data using frequency and cumulative-frequency tables, histograms, ogives, the mean and standard deviation, the five-number summary, box plots and outliers

Displaying and summarising one-variable data. Frequency and cumulative-frequency tables, histograms and ogives, the mean and standard deviation from data and a frequency table, the median, quartiles and IQR, the five-number summary, box and parallel box plots, the 1.5 IQR outlier rule and shape, with worked examples and traps.

18 min read →

How do we combine probabilities across several stages, and update a probability once we know something has happened?

Apply tree diagrams, conditional probability, independence and complementary events to solve multi-step probability problems

HSC Maths Advanced probability dot point. Sample spaces and the basic rules, complementary 'at least one' events, the addition rule, independent versus dependent events, multiplying along tree branches, conditional probability and Bayes-style reverse reasoning, with worked examples drawn from recent HSC questions.

18 min read →

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

Continuous random variables. Probability density functions, cumulative distribution functions, computing probabilities by integration, and finding mean, median, mode and variance, with worked examples.

15 min read →