Mistake Master
One Number Is the Target. The Other One Moves
You'll learnhow a parameter differs from a statistic and why the notation carries the whole distinction, what unbiased actually promises and what it does not, why variability is the property sample size controls, and why a bigger sample makes a biased design more confident instead of more correct.
A parameter is one number describing a population: fixed, and in any real problem never seen. A statistic is computed from a sample, known exactly the moment the data arrive, and different on the next sample. Every picture here is the same object — the exact distribution of the sample proportion across all possible samples — asked a different question. It shows an unbiased estimator landing 0.06 from the truth one week in ten, because unbiased is a promise about the center of that distribution and not about any single sample. Then the reverse trap: a volunteer poll centered at 0.70 when the truth is 0.50, where growing the sample from 500 to 8,000 raises the chance of landing within 0.01 of the wrong answer from 41% to 95% while the chance of landing near the truth stays under one in ten thousand. Sample size buys tightness, and it has no opinion at all about where. Twelve short steps; press Next for each one.