Which statement correctly differentiates statistics from parameters?

• A. Statistics describe data for a sample; parameters describe data for an entire population
• B. Statistics describe data for a population; parameters describe data for a sample
• C. Parameters describe data for a sample; statistics describe data for an entire population
• D. Statistics are used to summarize qualitative data

Answer: (A)

The main idea is that parameters describe data for an entire population, while statistics describe data for a sample. A parameter is a fixed, often unknown quantity that characterizes the whole population (for example, the population mean or population standard deviation). Because we usually can’t measure every member of the population, these values are not known exactly and are inferred. A statistic, on the other hand, is computed from the actual sample we collect (for example, the sample mean or sample proportion) and these values can vary from one sample to another. This distinction underpins how we estimate population characteristics: we use statistics to estimate unknown parameters.