Bias of an estimator

Bias is about the center of a sampling distribution, not its spread: an estimator is biased when its average value across all samples sits above or below the true parameter. The sample mean is unbiased because $E(\bar{x}) = \mu$ (the expected value of x-bar equals mu, the population mean), so it is right on average even though any one sample misses. The range of a sample, by contrast, is biased low, since a sample rarely contains both the population minimum and the population maximum. Collecting more data does not remove bias that comes from how the sample was chosen.