In Exercises 4 and 5, determine whether the number is a parameter or a statistic. Explain your reasoning.

In 2021, the median annual salary of a first-year chemist was \$58,700.

검증된 단계별 안내

Understand the difference between a parameter and a statistic: A parameter is a numerical value that describes a characteristic of a population, while a statistic is a numerical value that describes a characteristic of a sample drawn from the population.

Identify the context of the given number: The problem states that the median annual salary of a first-year chemist in 2021 was \$58,700.

Determine whether the number refers to the entire population or a sample: If the number represents all first-year chemists in 2021, it is a parameter. If it represents only a subset (sample) of first-year chemists, it is a statistic.

Analyze the phrasing of the problem: The problem does not explicitly mention that the number is based on a sample, so it is reasonable to assume it refers to the entire population of first-year chemists in 2021.

Conclude: Since the number likely represents the entire population, it is a parameter. If additional information were provided indicating it was based on a sample, it would instead be a statistic.

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영상 길이:

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Parameter

A parameter is a numerical value that summarizes a characteristic of a population. It is a fixed value that is usually unknown and can only be estimated through sample data. In the context of statistics, parameters are often denoted by Greek letters, such as μ for the population mean or σ for the population standard deviation.

Statistic

A statistic is a numerical value that summarizes a characteristic of a sample drawn from a population. Unlike parameters, statistics can vary depending on the sample selected and are used to estimate population parameters. Common examples include sample means (x̄) and sample proportions (p̂), which help infer characteristics about the larger population.

Median

The median is a measure of central tendency that represents the middle value in a data set when the values are arranged in ascending or descending order. If there is an even number of observations, the median is the average of the two middle numbers. It is particularly useful for understanding the distribution of salaries, as it is less affected by extreme values than the mean.

In Exercises 4 and 5, determine whether the number is a parameter or a statistic. Explain your reasoning.In 2021, the median annual salary of a first-year chemist was \$58,700.