Population (Statistics)
In short: Population, in statistics, names the complete collection of people, animals or things a question is about, as opposed to the smaller sample that is actually measured.
7th GradeStatistics7.SP.A.1
What is Population?
In statistics, the population covers every member of the collection a question asks about, and members need not be people. It could be all 8th graders in a district, every battery off a factory line, or each oak tree in a forest.
Measuring every member is often too slow or too costly, so analysts take a sample and use it to estimate a value for the whole collection. Wording matters: change who the question is about and the right group to study changes with it.
How to spot it
- A question concerns everyone or everything of one kind, like every student in a school district.
- The wording sets all against some, a census against a survey, or the whole against the sample.
- A claim about a full collection rests on data from only a slice of it.
- You must decide whom or what a survey result is allowed to describe.
The method
- Read the question and underline who or what it is about; that collection is the target.
- Describe it completely, with place and time, such as 8th graders in one district this year.
- Decide whether everyone can be measured; if not, plan a sample drawn from that collection.
- State conclusions about the target only, never about a different group.
Population: solved example
Problem
An Oregon district enrolls 1,260 eighth graders. A researcher measures the height of 60 of them, chosen by chance, to estimate the average height of all eighth graders there. Name the target group and the sample.
Solution
The question concerns all eighth graders in the district, so the population is the 1,260 eighth graders.
The 60 students whose heights were taken form the sample, about \(\frac{60}{1{,}260} \approx 4.8\%\) of the whole group.
Try it
Question 1
A bakery inspector weighs 25 loaves out of the 900 baked today. Which loaves make up the target group?
Show the answer
The 900 loaves baked today; the 25 weighed loaves are the sample.
Question 2
A poll calls 400 voters in one city to predict a state election. Does the polled group match the question?
Show the answer
No. The question concerns all voters in the state, but the polled group comes only from one city, so conclusions may be unreliable.
Population vs. Random Sample
The population is the full group the question is about, big or small. A sample is the part you collect data from. The first is fixed by the question; the second is chosen by the researcher. A good random sample is what lets its results speak for the whole group.
Keep going
Lessons
Worksheets and quizzes
- Random Sampling and Inference – Worksheet
- Random Sampling and Inference – Quiz
- Comparing Two Populations – Worksheet
- Comparing Two Populations – Quiz
Related words
Whole dictionary: A–Z · 7th Grade · Statistics