HomeQuestions by topicStandard 2Statistical Analysis
HSC-STD-2 · Statistical Analysis

Statistical Analysis

HSC HSC Mathematics Standard 2 · 2024 content registry · first HSC 2027

Official NSW Curriculum syllabus and implementation timeline ↗Download questions and solutions PDF
MS-S1MS-S2MS-S4MS-S5
Assessment evidence

What these examples cover

These examples show assessable skills, not an official HSC topic weighting or prediction. The 2024 NSW syllabuses have their first HSC examination in 2027; students sitting the 2026 HSC continue under the applicable 2017 syllabus.

Teacher check

Teacher verification note: check the mathematics, notation, permitted technology and syllabus fit for your cohort before classroom or assessment use.

3 deterministic examples

Statistical Analysis questions with worked solutions

Each question is generated from an existing curriq QDSL archetype at a fixed seed. Marks and catalog content mappings travel with the generated question.

Worked example 1

2 marksstd2-s2-2
Green frog population Sam tags 160 frogs. A later sample of 220 frogs contains 32 tagged frogs.
Part a · 2 marks

Estimate the total frog population using capture-recapture.

Worked solution

Answer: 1100

  1. Capture Recapture: 8/55
  2. Proportion: 1100

Catalog reference: std2_cssa25_capture_recapture · seed 41001

Worked example 2

2 marksstd2-s2-4
Two football matches A team has a 20% chance of winning each game. Outcomes of successive games are independent.
Part a · 2 marks

Calculate the probability that the team wins exactly one of its next two games.

Worked solution

Answer: 8/25

  1. Multi Stage Outcomes: 2
  2. Probability Sum: 8/25

Catalog reference: std2_bar25_exactly_one_win · seed 41001

Worked example 3

2 marksstd2-s5-1
Basketball scores Game scores are normally distributed with mean 122 and standard deviation 2. What percentage lie between 118 and 124?
Part a · 2 marks

Find the percentage using the empirical rule.

Worked solution

Answer: 163/2

  1. Standard Deviation Interval: [-2,1]
  2. Normal Probability: 163/2

Catalog reference: std2_asc25_normal_empirical_interval · seed 41001

Content mapping and common errors

Statistical Analysis content identifiers

MS-S1

Data Analysis

Represent, interpret and analyse data using tables, graphs and summary statistics including mean, median and standard deviation.

Common student mistakes
  • ·Confusing mean, median and mode when data is skewed
  • ·Using a population formula instead of sample standard deviation
  • ·Misreading box-and-whisker plots
MS-S2

Relative Frequency and Probability

Use relative frequency and theoretical probability to solve practical problems and model random experiments.

Common student mistakes
  • ·Confusing 'at least' with 'exactly' in probability problems
  • ·Not listing all outcomes in a sample space
MS-S4

Bivariate Data Analysis

Investigate relationships between two variables using scatterplots, correlation coefficients and lines of best fit.

Common student mistakes
  • ·Confusing correlation with causation
  • ·Incorrectly reading/interpolating from a line of best fit
MS-S5

The Normal Distribution

Apply the properties of the normal distribution and z-scores to interpret and compare data sets.

Common student mistakes
  • ·Forgetting to include both tails when using the 68-95-99.7 rule
  • ·Using wrong mean or SD when standardising

Source and methodology

Examples are deterministic curriq catalog generations from existing QDSL archetypes at the published fixed seed. The generator copies only student-facing prompts, mark allocations, topic mappings, display tables or options, checked answers and marking-path results into this resource.

Review the official NSW Curriculum source ↗

Other Standard 2 topics

Algebra
3 content identifiers
Measurement
4 content identifiers
Financial Mathematics
3 content identifiers
Networks
2 content identifiers

From the blog

Data
Using NESA Data to Plan HSC Maths Teaching
Practice
HSC Maths Past Papers by Topic
Diagnostics
HSC Maths Multiple-Choice Questions and Generator Workflow

Generate a Statistical Analysis worksheet in 30 seconds

Pick focus areas, set difficulty, and export a print-ready Standard 2 paper. Free during early access for NSW teachers.

Join the waitlist