Big Ideas Math Algebra 2, 2014
BI
Big Ideas Math Algebra 2, 2014 View details
3. Collecting Data
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Exercise 9 Page 614

A bias is an error that results in a misrepresentation of a whole population.

See solution.

Practice makes perfect

A town council wants to know whether residents support having an off-leash area for dogs in the town park. Eighty dog owners were surveyed at the park and asked whether they agree with the idea. Here, the population consists of all residents in the town and the sample of the 80 dog owners. 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.

The council asked residents who were already available at the park, so this is a convenience sample. The sample is biased because people asked are dog owners. Therefore, people who respond to the question are most likely have a strong opinion about the off-leash area for their dogs.