Unbiased Estimator 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.
Unbiased estimator
Sampling distributions
An unbiased estimator is a statistic whose average value across all samples equals the true parameter, so it has no systematic tendency to be too high or low.
An estimator is unbiased when its sampling distribution is centered on the parameter it estimates, though any single estimate still varies around that center. For example, the sample mean is unbiased for the population mean because (the expected value of x-bar equals mu). Likewise the sample proportion is unbiased for the population proportion, since (the expected value of p-hat equals p). Bias concerns where the sampling distribution is centered, not how spread out it is.
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.