Math Playground
Data

Sampling

Pick a small group to learn about a big one — without bias.

You don't drink the whole pot to check the soup — you taste a spoonful. But only if you stirred first. Sampling lets you learn about millions from a handful — as long as the handful is fair.

Sampling means studying a subset of a population to draw conclusions about the whole. Done right (randomly, representatively), a small sample is astonishingly accurate; done wrong, no sample size can save you.

Where you'll meet this

Polls, quality control, medical trials, census estimates, market research, A/B testing — you almost never measure everyone, so the quality of your sample is everything.

statisticspollingresearch
Quick check

A magazine surveys its own readers about whether people read magazines. The result will be biased because...

Good sampling methods

  • Simple random — everyone has an equal chance; the gold standard.
  • Stratified — split the population into groups, sample each in proportion.
  • Systematic — every kth member from a list.
  • Cluster — randomly pick whole groups (e.g. schools), survey everyone in them.
  • Avoid: convenience samples — 'whoever's nearby' — they bake in bias.
Your turn

Why was the famous 1936 'Literary Digest' poll — which predicted Landon would beat Roosevelt in a landslide — so wrong despite 2.4 million responses?

Try it

Name the main sampling biases to watch for.

Selection bias (sampling frame excludes part of the population), non-response bias (who refuses differs from who answers), voluntary-response bias (only the motivated reply — often the angry ones), and survivorship bias (you only see the survivors).

Watch out

A bigger sample does not fix a biased sample. It just gives you a more precise estimate of the wrong number. Randomness and representativeness come first; size second.

Before trusting any survey, ask: *who was sampled, how were they chosen, and who didn't respond?* Those three questions catch most bad polls.

Recap
  • Sampling = studying a subset to learn about the whole.
  • Random + representative beats large-but-biased every time.
  • Watch for selection, non-response, voluntary-response, and survivorship bias.