---
title: "Sampling Methods and Their Trade-offs"
description: "Compare simple random, systematic, stratified, quota and opportunity sampling by what each costs to run and what bias each risks, and describe the sampling frame a method needs."
canonical: https://lightmysky.com/learn/mathematics/sampling-methods-and-their-trade-offs-mt_aSsRQvnKa6
source: https://lightmysky.com/learn/mathematics/sampling-methods-and-their-trade-offs-mt_aSsRQvnKa6.md
retrieved: 2026-09-12
---

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# Sampling Methods and Their Trade-offs

Compare simple random, systematic, stratified, quota and opportunity sampling by what each costs to run and what bias each risks, and describe the sampling frame a method needs.

Subject: Mathematics · Area: Data & Statistics · Ages 16 to 17
Page: https://lightmysky.com/learn/mathematics/sampling-methods-and-their-trade-offs-mt_aSsRQvnKa6

## Ready when they can

- Describe how to take a systematic sample and what could go wrong with it
- Choose a method for a stated population and defend the choice
- Say what a census gives that no sample can

## Lesson: Choosing how to sample

A systematic sample walks down a list in equal steps after a random start. For 90 names from a roll of 900, the interval is 900 divided by 90, which is 10: pick a random start from 1 to 10, then take every 10th name. The trap is a hidden pattern in the list that repeats on the same cycle as your step, so you sample the same kind of member over and over.

Match the method to the population and the question, then name the trade off you accept. Rush hour and midday commuters differ, so stratify by time band: sampling inside each band is cheap and guarantees both crowds appear in fair shares. With 600 full time and 300 part time students in a sample of 90, take 60 full time and 30 part time, keeping the two to one split.

A census asks everyone, so there is no sampling error. It still costs more time and money than any sample, and it can still suffer nonresponse. That is what a census gives that no sample can: data on every member.

**Tip.** Never take the first names on a list or a crowd of volunteers and call it fair. Both favour whoever sits at the front, while a random start or a stratified split protects every group.

**Recap.** Step through lists with a random start, stratify across groups that differ, and remember a census buys everyone at a price.

## Practice

14 questions on this page, each with its working shown.

## Needs first

- [Populations, Samples and Bias](https://lightmysky.com/learn/mathematics/populations-samples-and-bias-mt_c7knRZy3Vt)
- [Stratified Sampling](https://lightmysky.com/learn/mathematics/stratified-sampling-mt_CWzOOk0609)

## Opens up

- [The Data Science Workflow](https://lightmysky.com/learn/computing/the-data-science-workflow-mt_99QNfiyQ55)
- [Sampling Distributions and the Central Limit Theorem](https://lightmysky.com/learn/mathematics/sampling-distributions-and-the-central-limit-theorem-mt_nugaEeUSii)
- [Cross-Validation and Honest Model Selection](https://lightmysky.com/learn/computing/cross-validation-and-honest-model-selection-mt_YG7X3HYCrT)