Which statement correctly distinguishes a population parameter from a sample statistic?

• A. Parameters are random variables estimated from data; statistics are fixed values.
• B. Parameters describe a population; statistics describe the population.
• C. Statistics are fixed values for the population; parameters are computed from a sample.
• D. A parameter is a fixed population value (e.g., mu, sigma); a statistic is computed from a sample (e.g., xbar, s).

Answer: (D)

Think about what describes the whole group versus what you actually calculate from data. A population parameter is a fixed value that would describe the entire population—things like the true mean mu or true standard deviation sigma. We may not know them, but they don’t change just because we take a sample.

A statistic is computed from the sample data, such as the sample mean xbar or the sample standard deviation s, and it depends on which individuals happen to be in that sample. Different samples can yield different statistics, which is why statistics are treated as random variables (varying across samples) while parameters are fixed constants for the population.

That’s why the statement about parameters being fixed population values and statistics being computed from a sample is the correct distinction. The other choices mix up describe-ness and fixedness: parameters aren’t random variables estimated from data, statistics aren’t fixed values for the population, and statistics don’t describe the population the way parameters do.