--- title: "Populations, Samples and Bias" description: "Tell a population from a sample, judge whether a way of collecting data is fair, and say how a biased sample bends the conclusion." canonical: https://lightmysky.com/learn/mathematics/populations-samples-and-bias-mt_c7knRZy3Vt source: https://lightmysky.com/learn/mathematics/populations-samples-and-bias-mt_c7knRZy3Vt.md retrieved: 2026-09-02 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Populations, Samples and Bias Tell a population from a sample, judge whether a way of collecting data is fair, and say how a biased sample bends the conclusion. Subject: Mathematics · Area: Data & Statistics · Ages 14 to 15 Page: https://lightmysky.com/learn/mathematics/populations-samples-and-bias-mt_c7knRZy3Vt ## Ready when they can - Name the population that a survey is trying to describe - Point out the bias in a method such as asking only people leaving a gym - Say what has to be true for a sample to count as random ## Lesson: Who the Sample Really Speaks For Twelve tomato plants along the fence, and you measured every single one. The line through them could speak for a plant nobody picked because the whole fence was on the paper. Wren Lane has about 900 members, and nobody is going to measure 900 people. So the crew asks some of them and hopes those answers stand for the rest. The whole group a question is about is the population. The smaller group you actually ask is the sample. Before a form goes anywhere, write the population down in plain words: people who hold a membership here, not every visitor, not every gardener in the county. *(drawing: Twenty members, and only the small group of four gets asked. Those four are the sample. All twenty are the population.)* A sample is biased when some members of the population are less likely to be picked than others. That is about the method, not about the people. Ask at the gym door and you hear from people who go to the gym, so the town's exercise figure comes out too high. Ask by email and you miss every member with no address on file. The bias is settled the moment you choose where to stand, before one answer is written down. It does not only lose people. It bends the answer in a direction you can usually name before you start. **Example.** Sam sets up at the Saturday market gate and comes back with 140 replies. Those are 140 people who were at Wren Lane on a Saturday morning, and only about 310 of the 900 members ever are. The other 590 had no chance. Standing there twice as long doubles the same voice. Size and fairness are separate things. Posting forms out instead hands the choosing to the members, and the pile comes back holding whoever cared enough to send it. So report the share who replied beside the result: 120 back from 400 forms is 30 percent. *(drawing: Three questions, in that order. The middle one is where most surveys quietly go wrong.)* A sample counts as random when every member of the population has the same chance of being chosen, and something with no opinion does the choosing. In practice: one numbered list of all 900 members and a random number generator. Deciding to take one member in every ten only fixes how many names the generator pulls out, 900 / 10 = 90, and leaves the chance equal for all of them. Whoever happens to walk past is not random, however unplanned it felt. A random sample can still come out lopsided by luck, and luck is not bias. Luck settles down as the sample grows. Bias does not. None of this is only about forms. The site logbook says how busy the park was, but volunteers wrote it up only on the days they were on shift. So the book is a sample that circumstances selected. Any record you did not collect yourself deserves the same question: what could have ended up in here, and what could not? **Recap.** The population is the whole group a claim is about, and the sample is the part you actually ask. A method is biased when some members are less likely to be picked than others, and collecting more answers the same way leaves the lean exactly where it was instead of curing it. Random means every member has the same chance, decided by something with no opinion. ## Practice 24 questions on this page, each with its working shown. ## Needs first - [Scatter Graphs](https://lightmysky.com/learn/mathematics/scatter-graphs-mt_BdAeZJUOir) ## Opens up - [Stratified Sampling](https://lightmysky.com/learn/mathematics/stratified-sampling-mt_CWzOOk0609)