Finally, describe the relationship of a sample to a population and classify your two samples as random, systematic, cluster, stratified, or convenience.
Question: Finally, describe the relationship of a sample to a population and classify your two samples as random, systematic, cluster, stratified, or convenience.
In statistics, a sample is a subset of a population that is used to represent the whole group as accurately as possible. A population is the entire group that we want to study or describe. For example, if we want to know the average height of people in a city, the population is all the people in the city, and the sample is a smaller group of people that we measure.
There are different ways to select a sample from a population. Some of the common methods are:
- Random sampling: Every member of the population has an equal chance of being selected. This method is unbiased and simple, but it may not be feasible or practical in some situations.
- Systematic sampling: We select every nth member of the population, where n is a fixed interval. For example, we can select every 10th person from a list of names. This method is easy and convenient, but it may introduce some bias if there is a pattern or order in the population.
- Cluster sampling: We divide the population into groups or clusters that are similar to each other, and then we select some of the clusters at random. For example, we can divide a city into neighborhoods and then randomly choose some neighborhoods to survey. This method is useful when the population is large and spread out, but it may reduce the accuracy and precision of the estimates.
- Stratified sampling: We divide the population into groups or strata that are different from each other, and then we select some members from each stratum at random. For example, we can divide a city into age groups and then randomly choose some people from each age group to survey. This method is useful when we want to compare different subgroups of the population, but it may require more time and resources to implement.
- Convenience sampling: We select members of the population that are easily accessible or available. For example, we can survey people who are walking on the street or shopping in a mall. This method is quick and cheap, but it may be very biased and unrepresentative of the population.
In our case, we have two samples: one from School A and one from School B. We can classify them as follows:
- The sample from School A is a **stratified sample**, because we divided the students into grades and then randomly selected 10 students from each grade.
- The sample from School B is a **convenience sample**, because we surveyed the students who were present in the cafeteria during lunch time.
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