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Problem-Solving and Data AnalysisMediumWhy a small random sample is useful

Problem-Solving and Data Analysis practice question

A city has about 5 million residents. A survey asks 1,000 residents, selected at random, about their commutes. Which of the following best explains why the survey's results are useful?

  1. A. Random selection makes the sample resemble the whole population, so the results can be generalised to the city, within a margin of error.Correct
  2. B. 1,000 people is a large fraction of the city's population.
  3. C. Every resident of the city was given the chance to answer.
  4. D. A random sample has no sampling error at all.

Answer: A. Random selection makes the sample resemble the whole population, so the results can be generalised to the city, within a margin of error.

The value of a random sample comes from how it is chosen, not from its size relative to the population; it estimates the population with a quantifiable margin of error.

Why the other answers are wrong

B. 1,000 people is a large fraction of the city's population.
1,000 is a tiny fraction of 5 million — and that isn't what makes the sample useful.
C. Every resident of the city was given the chance to answer.
Only 1,000 residents were asked; the rest were not.
D. A random sample has no sampling error at all.
Random samples do have sampling error; that's what the margin of error measures.

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