"Determine whether the data set is a population or a sample. Explain your reasoning.
A survey of 250 members from an organized union of over 20,000 members"

Verified step by step guidance

1. Step 1: Understand the definitions of population and sample. A population refers to the entire group of individuals or items that you want to study, while a sample is a subset of the population selected for analysis.
2. Step 2: Identify the total size of the group being studied. In this case, the organized union consists of over 20,000 members, which represents the population.
3. Step 3: Examine the size of the group surveyed. The problem states that only 250 members were surveyed, which is a subset of the total population.
4. Step 4: Compare the surveyed group to the population. Since the surveyed group (250 members) is smaller than the total population (20,000 members), it is considered a sample.
5. Step 5: Conclude that the data set is a sample because it represents only a portion of the entire population, and explain that samples are often used to make inferences about the population when studying the entire population is impractical.

Key Concepts

Population

In statistics, a population refers to the entire group of individuals or items that we are interested in studying. It encompasses all members of a defined group, such as all employees in a company or all voters in an election. Understanding whether a data set represents a population is crucial for determining the scope and applicability of statistical analyses.

Sample

A sample is a subset of a population that is selected for analysis. It is used to make inferences about the larger population without needing to collect data from every member. The quality of a sample can significantly affect the validity of conclusions drawn, making it essential to ensure that the sample is representative of the population.

Sampling Method

The sampling method refers to the technique used to select individuals from a population to form a sample. Common methods include random sampling, stratified sampling, and convenience sampling. The choice of sampling method impacts the reliability of the results and the extent to which they can be generalized to the population.