Sample vs Statistic
Both terms below come up in the same part of the course, and students mix them up. Here is each one defined on its own, side by side, so you can see where they part company.
Sample
Collecting data and study design
A sample is the subset of a population that you actually collect data from in order to estimate something about the whole population.
Because measuring an entire population is often impossible, you gather data from a smaller sample and use it to make estimates. For example, polling 1,000 voters to estimate how all voters will act treats those 1,000 people as the sample. A numerical summary of a sample, such as the sample mean (written , read as x-bar), is called a statistic. A well-chosen random sample lets that statistic stand in for the unknown population value.
Statistic
Collecting data and study design
A statistic is a numerical value computed from sample data, used to estimate a corresponding population parameter.
A statistic varies from sample to sample because it depends on which individuals you happen to select. For example, if 52 out of 100 sampled voters favor a measure, the sample proportion is (p-hat, the estimate of the population proportion). Common statistics include the sample mean (x-bar) and the sample standard deviation . Its value changes with each new sample, which is what sampling distributions describe.