Key takeaway: A population in statistics is the entire group of people, animals or objects that a study wants to describe, from which a smaller sample may be drawn.
Grade 77.SP.A.1Statistics and Data
Definition of Population
A population in statistics is the complete collection of individuals you care about, whether they are voters in a town, batteries made in a factory or trees in a park. It does not have to be people, and it is not a number: it is the whole group itself.
Because measuring every member is often impossible, statisticians study a sample, a smaller part of the population. A number that describes a whole population is a parameter. A number that describes a sample is a statistic, and it is used to estimate the parameter. Deciding who belongs in the population is the first step of any study.
Formula and notation
Population size is written \(N\) and sample size \(n\), with \(n \le N\). A sample proportion gives an estimate for the population:
\[\hat{p} = \frac{\text{number with the trait in the sample}}{n}\]
The estimated population count is \(\hat{p} \cdot N\).
Key facts
- A population in statistics is defined by what the question asks, such as all voters in one city.
- Any kind of thing can form a population: people, plants, products or events.
- A number describing the whole group is a parameter; one from a sample is a statistic.
- Sampling makes studying huge groups practical, but it adds some uncertainty.
Population example
A town has 12,400 registered voters. A pollster phones a random group of 310 of them, and 124 say they support building a new skate park. Name the population and the sample, and estimate how many voters support the park.
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Population: all 12,400 registered voters. Sample: the 310 voters who were phoned.
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Sample proportion: \(\frac{124}{310} = 0.40\).
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Estimate for the population: \(0.40 \times 12400 = 4960\).
About 4,960 voters are estimated to support the skate park.
Common mistake
Watch out
Asked for the population in the voter poll, Camille answers “310, the number of people who answered the phone.”
Why it is wrong
She named the sample and gave only its size. The population in statistics is the whole group the poll wants to describe, all 12,400 registered voters. A population is a group of individuals, not a count, and it is always at least as large as the sample.
Related terms and lessons
Browse the glossary: A–Z list · Grade 7 vocabulary · Statistics and Data