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 614

In both types of samples a population is divided into smaller groups.

See solution.

Practice makes perfect

We are asked to describe the difference between a stratified sample and a cluster sample. Before we do this, let's recall the definitions of each of these sample types.

Stratified Sample

When we want to create a stratified sample, we should divide a population into smaller groups that share a similar characteristic — for example, the type of job they have or their marital status.

After we divide our population, our sample will contain randomly selected members from each group.

By using stratified sampling we are sure that people with each characteristic are represented in the final sample.

Cluster Sample

To create a cluster sample we also need to divide a population into groups that are called clusters. Here, members of each cluster are chosen randomly.

Next, when our population is divided into smaller groups, our sample will contain one or more of the clusters. A cluster or clusters that will be in the final sample are also chosen randomly.

Since members of each cluster are chosen randomly, the final sample should also be random.

Comparison

Finally we are ready to compare these two types of samples. Notice that in both of them the first step requires dividing a population into smaller groups.

Stratified Sample Cluster Sample
Division Into Groups Members share a similar characteristic. Members are chosen randomly.
Sample Selection Randomly selected members from each group. Randomly selected cluster or clusters.

Both ways of sampling should result in a final sample that is random.