In the context of probability and statistics, what is the main difference between a $\mathrm{parameter}$ and a $\mathrm{statistic}$?

• A. A $\mathrm{parameter}$ is a numerical value that describes a characteristic of a population, while a $\mathrm{statistic}$ is a numerical value that describes a characteristic of a sample.
• B. A $\mathrm{parameter}$ is calculated from sample data, while a $\mathrm{statistic}$ is calculated from population data.
• C. A $\mathrm{parameter}$ and a $\mathrm{statistic}$ are both calculated from the entire population.
• D. A $\mathrm{parameter}$ is always unknown, while a $\mathrm{statistic}$ is always known and fixed.

Answer: (A)

Verified step by step guidance

1. Step 1: Understand the definitions of 'parameter' and 'statistic' in statistics. A parameter is a numerical value that describes a characteristic of an entire population, such as the population mean or population proportion.
2. Step 2: Recognize that a statistic is a numerical value calculated from a sample, which is a subset of the population. For example, the sample mean or sample proportion are statistics.
3. Step 3: Note that parameters are generally fixed but often unknown because it is usually impractical to measure the entire population, whereas statistics are known values computed from the sample data.
4. Step 4: Differentiate between the two by remembering that parameters describe populations, and statistics describe samples. This distinction is fundamental in inferential statistics, where statistics are used to estimate parameters.
5. Step 5: Summarize the main difference: a parameter is a numerical characteristic of a population (usually unknown), while a statistic is a numerical characteristic of a sample (known and used to estimate the parameter).