Is Topic 6.4 directly tested in the exam?

Topic 6.4 is labelled “for teaching and learning only” in the official syllabus, so standalone questions specifically on sampling theory are unlikely. However, the key ideas - \$E(\bar\{X\}) = \mu\$, \$\operatorname\{Var\}(\bar\{X\}) = \sigma^2/n\$, and unbiased estimation - appear inside Topic 6.5 Hypothesis Testing questions, so you must know them well.

Can I use the GC to compute \$\bar\{x\}\$ and \$s^2\$ from raw data?

Yes. Use 1-Var Stats on a TI or STAT mode on a Casio to obtain \$\bar\{x\}\$ and \$s_x\$ directly. For summarised data (given \$\sum x\$ and \$\sum x^2\$), show the manual substitution formula in working alongside the GC result.

When do I need to use the CLT versus the exact normal distribution?

If the original population is stated to be normal, \$\bar\{X\}\$ is exactly normal for any sample size \$n\$. Use the CLT only when the population distribution is unknown or non-normal, and only when \$n\$ is large. Always state which case applies. ---

Study guide07 Oct 2025, 00:00 Z

H2 Maths Sampling Notes | CLT & Sample Distributions

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H2 Maths sampling notes: key formulas and worked examples for sample mean distributions, Central Limit Theorem, and unbiased estimation in exams.

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Reviewed by

Marcus Pang·Managing Director (Maths)

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Quick sampling map
Sampling Language
Distribution of the Sample Mean
Unbiased Estimates from Summarised Data

Q: What does H2 Maths Notes (JC 1-2): 6.4) Sampling cover?
A: Sample mean distributions, Central Limit Theorem (CLT), and unbiased-estimation workflows aligned with the H2 Maths 2026 syllabus.

Before you revise
SEAB labels sub-topic 6.4 Sampling as "for teaching and learning only", but the core ideas (sample mean, $E(\bar{X})$ , $\operatorname{Var}(\bar{X})$ , CLT) are exactly what you use inside 6.5 Hypothesis Testing. Recap mean/variance notation and get comfortable computing $\bar{x}$

If you have...	Walk away with this	First action
1 second	A sample is a small window into a population.	Identify the population parameter.
10 seconds	The sample mean varies less when sample size is larger.	Divide the variance by n for the sample mean.
100 seconds	CLT lets large samples behave approximately normal.	State whether normality is exact or approximate.

H2 Maths Sampling Notes | CLT & Sample Distributions

Quick sampling map

Sampling Language

Distribution of the Sample Mean

Unbiased Estimates from Summarised Data

Calculator Workflows

Exam Watch Points

Practice Quiz

Quick Revision Checklist

Common exam mistakes

Frequently asked questions

Sources

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