Define the terms parameter and statistic. Be sure that the concepts of population and sample are included in your definitions.

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The terms "parameter" and "statistic" are related to the field of statistics and are commonly used to describe numerical characteristics of data sets. It is important to understand the concepts of population and sample in order to properly define these terms.

A population refers to the entire set of individuals, objects, or events that we are interested in studying or making inferences about. For example, if we are conducting a survey to determine the average height of all adults living in a city, the population would be the complete set of adults in that city.

On the other hand, a sample is a subset or a smaller representative group selected from the population. In our previous example, instead of measuring the height of every adult in the city, we might randomly select a sample of 500 adults to gather our data. The purpose of using a sample is to make it feasible and more efficient to collect information about the entire population.

Now, let's define the terms "parameter" and "statistic" in light of the population and sample concepts:

1. Parameter: A parameter is a numerical characteristic or measure that describes a specific feature of a population. It is typically denoted using Greek symbols, such as μ (mu) for population mean, σ (sigma) for population standard deviation, and p for population proportion. Parameters are usually unknown and their values are often estimated using sample statistics. For example, the average height (μ) of all adults in a city is a population parameter.

2. Statistic: A statistic is a numerical measure that describes a specific feature of a sample. It is often used as an estimate of the corresponding population parameter. Common statistics include the sample mean (x̄), sample standard deviation (s), and sample proportion (p̂). These values are calculated from data collected within the sample. For instance, the average height (x̄) of the adults within a sample would be a sample statistic.

In summary, a parameter refers to a numerical characteristic describing the entire population, while a statistic is a numerical measure used to estimate the corresponding population parameter based on information obtained from a sample. The distinction between these terms is crucial in statistical analysis as it helps us to generalize findings from a sample to the larger population.