Representative samples — Data, 14–17 years
How to learn about a large group by studying a smaller, fairly chosen group. Data, 14–17 years.
The idea
A sample is a smaller group chosen to tell us something about a larger group, called the population. It is useful only when the sample resembles that population in the ways that matter. Asking 100 randomly chosen students can say more about a school than asking the first 100 students through one doorway.
Why we need it
Usually we cannot ask every person, measure every tree or test every product: it would take too long, cost too much, or cause damage. Sampling solves this problem by using a manageable part of the population. The difficulty is that a badly chosen sample can give a precise-looking answer that is still unfairly biased.
Worked example
A school has 800 students and wants to estimate how many cycle to school. First, number all 800 names. Next, use a random method to choose 80 names, rather than choosing friends or people from the bicycle racks. If 24 of the 80 cycle, the sample proportion is 24/80 = 30%. The school estimates about 30% of all 800, or 240 students, cycle to school.
The common trap
A common mistake is to think that a larger sample is automatically a better sample. Size matters, but selection matters first: asking 1,000 football fans about the whole population may be less useful than asking 100 people chosen fairly. The mistake is reasonable because more measurements usually feel like more evidence, yet repeated bias does not become fairness.
Where it is used
Pollsters use samples to estimate opinions before an election, and companies use them to test whether customers like a product. Scientists sample river water or soil instead of disturbing an entire ecosystem. The result is an estimate, not a guarantee, so careful reports include how people were chosen and how uncertain the estimate may be.
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