## Characteristics of Estimators

This section discusses two important characteristics used as point estimates of parameters: bias and sampling variability. Bias refers to whether an estimator tends to over or underestimate the parameter. Sampling variability refers to how much the estimate varies from sample to sample.

### Answers

- You tried to estimate where the donkey's tail should have gone. Your estimates were biased because you did not pin them on the correct spot; they were uniformly too low. However, your estimates did not vary much because they were all close to each other.
- Bias refers to whether an estimator tends to either over or
underestimate the parameter. In this case, the estimator with the
sampling distribution with a mean of 8 is the most biased because it
tends to be the most different from the population parameter.
- A statistic's sampling variability is usually measured by its standard
error; the smaller the standard error, the less the sampling
variability. In this case, the sampling distribution with a standard
error of 2 has
the least sampling variability.
- Although this is a fictional parameter, the same thing applies. A statistic is unbiased if the mean of the sampling distribution of the statistic, also known as the expected value, is equal to the parameter. Therefore, an unbiased statistic would have an expected value of 9.