Big Ideas Math Algebra 2, 2014
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Big Ideas Math Algebra 2, 2014 View details
3. Collecting Data
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Exercise 1 Page 611

A population consists of all the members of a group of interest. A sample is a subset of the population.

Cluster sample

Practice makes perfect

A population consists of all the members of a group of interest. Since it may be impractical to examine every member of a population, a sample — a subset of the population — is sometimes selected to represent the population. The sample can then be analyzed to draw conclusions about the entire population.

Let's consider our situation.

The students in the school are divided according to their zip codes. Then, all of the students that live in one zip code are selected.

Here, the population consists of all of the students. The sample consists of the students who live in one zip code. Samples can be classified into different categories.

Name Characteristic
Random Sample Each member of the population has an equal chance of being selected.
Self-selected Sample Members volunteer to be included in the sample.
Systematic Sample Members are selected according to a specified interval from a random starting point.
Stratified Sample The population is first divided into smaller groups that share a similar characteristic. Members are then randomly selected from each group.
Cluster Sample The population is first divided into groups, called clusters. All of the members in one or more of the clusters are selected.
Convenience Sample Members that are readily available or easy to reach are selected.

In our situation, students are divided into groups based on their zip code. Then, all of the students from one of those groups are selected as a sample. This means that we have a cluster sample.