What is a population in statistics?
A population in statistics is the whole group of people, animals or objects you want to learn about, such as every student in a school or every bulb a factory makes. Measuring all of them is often too costly, so you study a sample, a part of the population, and use it to draw conclusions about the whole group.
Population in a picture
Formal definition and notation
A population is the complete set of individuals (people, objects, events or measurements) that a statistical question is about. A number that describes the whole population, such as its mean μ or proportion p, is a parameter. A number computed from a sample, such as x̄ or p̂, is a statistic and is used to estimate the parameter. Conclusions from a sample apply to a population only if the sample is representative of it, which random sampling tends to produce.
| Symbol | Read it as | Meaning |
|---|---|---|
| N | capital N | the number of individuals in the population (n for a sample) |
| μ | mew | the population mean, a parameter |
| p | p | the population proportion; the sample proportion is p̂ |
Key facts
- The population is set by the question: “all US teens,” “all trout in Lake X” or “all cars made in March.”
- Studying every member of a population is a census.
- Population numbers are parameters; sample numbers are statistics.
- A sample must be representative of the population for its results to carry over; random selection helps.
- Results describe only the population that was sampled: a survey of one school says little about all US students.
- The statistics meaning differs from the everyday one: a population can be cars, test scores or light bulbs, not just people living in a place.
Population examples, step by step
Example 1: Name the population and the sample
A pollster surveys 200 of the 8,000 registered voters in a town about a new park. Name the population and the sample, and find what percent of the population was surveyed.
- Population: all 8,000 registered voters in the town. Sample: the 200 voters surveyed.
- Percent surveyed: 2008000 = 0.025.
- 0.025 = 2.5%.
Answer: The population is all 8,000 voters, the sample is the 200 surveyed, and 2.5% of the population was surveyed.
Example 2: Estimate a population count
In a random sample of 150 students at a school of 1,200, 60 walk to school. Estimate how many students in the whole school walk.
- Sample proportion: 60150 = 0.4.
- Assume the population proportion is about the same: 0.4 × 1200 = 480.
Answer: About 480 students in the school walk to school.
Example 3: Estimate the size of a population
To estimate the number of fish in a pond, biologists tag 40 fish and release them. Later they catch 50 fish, and 8 of them are tagged. Estimate the fish population.
- In the second catch, 850 of the fish are tagged.
- Assume the same share of the whole population is tagged: 40N = 850.
- Cross-multiply: 8N = 40 × 50 = 2000, so N = 250.
Answer: There are about 250 fish in the pond.
Common mistakes
The population is defined by the question, not by who was measured.
Statistics from samples estimate parameters; they vary from sample to sample.
To speak about a bigger population, sample from that bigger population.
Not to be confused with
A sample is part of the population that is actually measured: 200 voters out of 8,000.
In everyday speech, population means how many people live in a place. In statistics it is any complete group being studied, such as all the bolts a machine made today.
Quick check: 3 questions
A researcher measures 40 trout from Lake Pine to estimate the average length of trout in Lake Pine. What is the population?
Answer: B. The question is about every trout in Lake Pine, so they are the population. The 40 trout are the sample, the average length is the parameter being estimated, and the lake is just the place.Show answer and explanation
In a random sample of 50 light bulbs from a batch of 5,000, 2 are defective. About how many bulbs in the batch are defective?
Answer: C. 250 = 0.04, and 0.04 × 5000 = 200. 2 is only the sample count, 100 uses 2 out of 100, and 2,500 confuses the batch with half of it.Show answer and explanation
Which number describes a population?
Answer: C. Every player in the league is the whole group, so their mean height is a parameter. The other three come from samples, so they are statistics.Show answer and explanation
Population: frequently asked questions
What is the difference between a population and a sample?
The population is the whole group you want to know about. A sample is the part of it you actually measure. If you want the average sleep time of all 900 students in a school, those 900 are the population; the 60 you survey are a sample. Good samples are chosen at random so they represent the population.
Why not just study the whole population?
Often it is too expensive, too slow or impossible. You cannot interview every voter in a country before an election, and testing every match in a factory by burning it would destroy the product. A well-chosen random sample gives a close estimate for much less effort. Studying the whole population is called a census.
Practice and tools
Sources
- Common Core State Standards, Grade 7 Statistics and Probability (7.SP.A.1)
- OpenStax, Introductory Statistics 2e, 1.1 Definitions of Statistics, Probability, and Key Terms
- Common Core State Standards, High School Statistics and Probability, Making Inferences and Justifying Conclusions (HSS-IC.A.1)
Updated November 2026·Reviewed by the Effortless Math team·Standards: CCSS 7.SP.A.1, CCSS HSS-IC.A.1
Cite this entry
Effortless Math Team. “Population.” Effortless Math Dictionary. Updated November 2026. https://www.effortlessmath.com/math-dictionary/population/
Flashcard
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