# 9709 P6 Sampling and estimation Topic Questions

> CIE IAL 9709 P6: every Sampling and estimation topic question from 49 papers (2020–2026), grouped by syllabus point. 187 questions, 517 marks, with direct…

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CIE IAL · Mathematics · 9709 P6 · A Level

Every 9709 P6 Sampling and estimation topic question from the 2020–2027 syllabus, drawn from 49 papers (2020–2026) and grouped by syllabus point. Each row opens a page listing the exact question numbers, marks and a direct link into the paper. These are questions by topic, not full papers, so you can revise one topic at a time.

- 9709 P6
- 8 subtopics
- 187 topic questions
- 49 papers
- 517 tagged marks
- [Back to Sampling and estimation](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/sampling-and-estimation/)
- [All paper codes](https://www.examsci.com/topics/)

Core finding

**calculate unbiased estimates of the population mean and variance from… is the most frequently assessed subtopic in Sampling and estimation, with 38 topic questions and 141 marks across 35 papers.** determine and interpret a confidence interval for a… follows with 31 topic questions and 93 marks. The topic contains 8 subtopics, 187 topic questions and 517 marks in total. Rows count only the parts tagged to that subtopic, keep the same colour in both charts and repeat paper count, tagged marks and year range in the native table.

## Topic question count and mark distribution

Subtopics are on the vertical axis and sorted from highest to lowest. Only the parts whose knowledge graph matches a subtopic are counted for it, and percentages are each row's share of the tagged total in that chart. A part tagged to several subtopics is counted in each bar, so the bars are not a partition of the topic total.

### Questions by subtopic

question items

- [• calculate unbiased estimates of the population mean and variance from a sample, using either raw or summarised data](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/sampling-and-estimation/calculate-unbiased-estimates-of-the-population-mean-and-variance-from-a-sample-using/) (35 papers) — 38 · 21.1%
- [• determine and interpret a confidence interval for a population mean in cases where the population is normally distributed with known variance or where a large sample is used](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/sampling-and-estimation/determine-and-interpret-a-confidence-interval-for-a-population-mean-in-cases-where/) (20 papers) — 31 · 17.2%
- [• determine, from a large sample, an approximate confidence interval for a population proportion](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/sampling-and-estimation/determine-from-a-large-sample-an-approximate-confidence-interval-for-a-population/) (18 papers) — 27 · 15.0%
- [• use the Central Limit Theorem where appropriate](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/sampling-and-estimation/use-the-central-limit-theorem-where-appropriate/) (19 papers) — 25 · 13.9%
- [• recognise that a sample mean can be regarded as a random variable, and use the facts that $\mathrm{E}(\bar{X})=\mu$ and that $\operatorname{Var}(\bar{X})=\frac{\sigma^2}{n}$](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/sampling-and-estimation/recognise-that-a-sample-mean-can-be-regarded-as-a-random-variable-and-use-the-facts/) (19 papers) — 22 · 12.2%
- [• use the fact that $(\bar{X})$ has a normal distribution if $X$ has a normal distribution](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/sampling-and-estimation/use-the-fact-that-bar-x-has-a-normal-distribution-if-x-has-a-normal-distribution/) (11 papers) — 14 · 7.8%
- [• understand the distinction between a sample and a population, and appreciate the necessity for randomness in choosing samples](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/sampling-and-estimation/understand-the-distinction-between-a-sample-and-a-population-and-appreciate-the/) (9 papers) — 13 · 7.2%
- [• explain in simple terms why a given sampling method may be unsatisfactory](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/sampling-and-estimation/explain-in-simple-terms-why-a-given-sampling-method-may-be-unsatisfactory/) (10 papers) — 10 · 5.6%

### Marks by subtopic

marks

- [• calculate unbiased estimates of the population mean and variance from a sample, using either raw or summarised data](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/sampling-and-estimation/calculate-unbiased-estimates-of-the-population-mean-and-variance-from-a-sample-using/) (35 papers) — 141 · 27.1%
- [• determine and interpret a confidence interval for a population mean in cases where the population is normally distributed with known variance or where a large sample is used](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/sampling-and-estimation/determine-and-interpret-a-confidence-interval-for-a-population-mean-in-cases-where/) (20 papers) — 93 · 17.9%
- [• determine, from a large sample, an approximate confidence interval for a population proportion](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/sampling-and-estimation/determine-from-a-large-sample-an-approximate-confidence-interval-for-a-population/) (18 papers) — 89 · 17.1%
- [• recognise that a sample mean can be regarded as a random variable, and use the facts that $\mathrm{E}(\bar{X})=\mu$ and that $\operatorname{Var}(\bar{X})=\frac{\sigma^2}{n}$](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/sampling-and-estimation/recognise-that-a-sample-mean-can-be-regarded-as-a-random-variable-and-use-the-facts/) (19 papers) — 73 · 14.0%
- [• use the Central Limit Theorem where appropriate](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/sampling-and-estimation/use-the-central-limit-theorem-where-appropriate/) (19 papers) — 55 · 10.6%
- [• use the fact that $(\bar{X})$ has a normal distribution if $X$ has a normal distribution](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/sampling-and-estimation/use-the-fact-that-bar-x-has-a-normal-distribution-if-x-has-a-normal-distribution/) (11 papers) — 41 · 7.9%
- [• understand the distinction between a sample and a population, and appreciate the necessity for randomness in choosing samples](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/sampling-and-estimation/understand-the-distinction-between-a-sample-and-a-population-and-appreciate-the/) (9 papers) — 18 · 3.5%
- [• explain in simple terms why a given sampling method may be unsatisfactory](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/sampling-and-estimation/explain-in-simple-terms-why-a-given-sampling-method-may-be-unsatisfactory/) (10 papers) — 11 · 2.1%

## Subtopic comparison matrix

Curriculum order is by syllabus number, then alphabetically. Every row links to the matching past-paper question list.

| Subtopic | Topic questions | Papers | Marks | Years | |
| --- | --- | --- | --- | --- | --- |
| **[• calculate unbiased estimates of the population mean and variance from a sample, using either raw or summarised data](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/sampling-and-estimation/calculate-unbiased-estimates-of-the-population-mean-and-variance-from-a-sample-using/)** | 38 | 35 | 141 | 2020–2026 | [Open topic questions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/sampling-and-estimation/calculate-unbiased-estimates-of-the-population-mean-and-variance-from-a-sample-using/) |
| **[• determine and interpret a confidence interval for a population mean in cases where the population is normally distributed with known variance or where a large sample is used](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/sampling-and-estimation/determine-and-interpret-a-confidence-interval-for-a-population-mean-in-cases-where/)** | 31 | 20 | 93 | 2020–2026 | [Open topic questions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/sampling-and-estimation/determine-and-interpret-a-confidence-interval-for-a-population-mean-in-cases-where/) |
| **[• determine, from a large sample, an approximate confidence interval for a population proportion](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/sampling-and-estimation/determine-from-a-large-sample-an-approximate-confidence-interval-for-a-population/)** | 27 | 18 | 89 | 2020–2026 | [Open topic questions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/sampling-and-estimation/determine-from-a-large-sample-an-approximate-confidence-interval-for-a-population/) |
| **[• explain in simple terms why a given sampling method may be unsatisfactory](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/sampling-and-estimation/explain-in-simple-terms-why-a-given-sampling-method-may-be-unsatisfactory/)** | 10 | 10 | 11 | 2020–2026 | [Open topic questions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/sampling-and-estimation/explain-in-simple-terms-why-a-given-sampling-method-may-be-unsatisfactory/) |
| **[• recognise that a sample mean can be regarded as a random variable, and use the facts that $\mathrm{E}(\bar{X})=\mu$ and that $\operatorname{Var}(\bar{X})=\frac{\sigma^2}{n}$](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/sampling-and-estimation/recognise-that-a-sample-mean-can-be-regarded-as-a-random-variable-and-use-the-facts/)** | 22 | 19 | 73 | 2020–2026 | [Open topic questions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/sampling-and-estimation/recognise-that-a-sample-mean-can-be-regarded-as-a-random-variable-and-use-the-facts/) |
| **[• understand the distinction between a sample and a population, and appreciate the necessity for randomness in choosing samples](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/sampling-and-estimation/understand-the-distinction-between-a-sample-and-a-population-and-appreciate-the/)** | 13 | 9 | 18 | 2020–2025 | [Open topic questions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/sampling-and-estimation/understand-the-distinction-between-a-sample-and-a-population-and-appreciate-the/) |
| **[• use the Central Limit Theorem where appropriate](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/sampling-and-estimation/use-the-central-limit-theorem-where-appropriate/)** | 25 | 19 | 55 | 2020–2026 | [Open topic questions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/sampling-and-estimation/use-the-central-limit-theorem-where-appropriate/) |
| **[• use the fact that $(\bar{X})$ has a normal distribution if $X$ has a normal distribution](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/sampling-and-estimation/use-the-fact-that-bar-x-has-a-normal-distribution-if-x-has-a-normal-distribution/)** | 14 | 11 | 41 | 2021–2026 | [Open topic questions](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/sampling-and-estimation/use-the-fact-that-bar-x-has-a-normal-distribution-if-x-has-a-normal-distribution/) |

## Browse every topic question

- [• calculate unbiased estimates of the population mean and variance from a sample, using either raw or summarised data](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/sampling-and-estimation/calculate-unbiased-estimates-of-the-population-mean-and-variance-from-a-sample-using/) — 38 question items · 35 papers — 141 marks · 2020–2026
- [• determine and interpret a confidence interval for a population mean in cases where the population is normally distributed with known variance or where a large sample is used](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/sampling-and-estimation/determine-and-interpret-a-confidence-interval-for-a-population-mean-in-cases-where/) — 31 question items · 20 papers — 93 marks · 2020–2026
- [• determine, from a large sample, an approximate confidence interval for a population proportion](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/sampling-and-estimation/determine-from-a-large-sample-an-approximate-confidence-interval-for-a-population/) — 27 question items · 18 papers — 89 marks · 2020–2026
- [• explain in simple terms why a given sampling method may be unsatisfactory](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/sampling-and-estimation/explain-in-simple-terms-why-a-given-sampling-method-may-be-unsatisfactory/) — 10 question items · 10 papers — 11 marks · 2020–2026
- [• recognise that a sample mean can be regarded as a random variable, and use the facts that $\mathrm{E}(\bar{X})=\mu$ and that $\operatorname{Var}(\bar{X})=\frac{\sigma^2}{n}$](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/sampling-and-estimation/recognise-that-a-sample-mean-can-be-regarded-as-a-random-variable-and-use-the-facts/) — 22 question items · 19 papers — 73 marks · 2020–2026
- [• understand the distinction between a sample and a population, and appreciate the necessity for randomness in choosing samples](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/sampling-and-estimation/understand-the-distinction-between-a-sample-and-a-population-and-appreciate-the/) — 13 question items · 9 papers — 18 marks · 2020–2025
- [• use the Central Limit Theorem where appropriate](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/sampling-and-estimation/use-the-central-limit-theorem-where-appropriate/) — 25 question items · 19 papers — 55 marks · 2020–2026
- [• use the fact that $(\bar{X})$ has a normal distribution if $X$ has a normal distribution](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/sampling-and-estimation/use-the-fact-that-bar-x-has-a-normal-distribution-if-x-has-a-normal-distribution/) — 14 question items · 11 papers — 41 marks · 2021–2026

## Other topics in 9709 P6

- [Continuous random variables 146 question items](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/continuous-random-variables/)
- [Hypothesis tests 206 question items](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/hypothesis-tests/)
- [Linear combinations of random variables 109 question items](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/linear-combinations-of-random-variables/)
- [The Poisson distribution 207 question items](https://www.examsci.com/topics/cie-ial/mathematics/9709-p6/the-poisson-distribution/)

## Topic question rules and edge cases

**How many subtopics does Sampling and estimation contain?**

This page lists 8 subtopics tagged to the current syllabus. They are ordered by syllabus number, then alphabetically, and each row opens a page of matching past-paper questions.

**How are the subtopic question and mark totals calculated?**

A multiple-choice question contributes one item and its marks to every subtopic it is tagged with. A structured question contributes one item per tagged part, and that part’s marks; untagged parts of the same question are not counted here. A part tagged to several subtopics therefore appears under each of them.

**Why do some subtopics have no numbered prefix?**

Practical-skills statements and some syllabus bullets are unnumbered. Numbered statements come first; unnumbered statements and ties are sorted alphabetically.

**Is the LaTeX rendered without JavaScript?**

Yes. Subtopics that contain formulas are converted to static KaTeX HTML during the build, and the KaTeX stylesheet is served from the same site.

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