Three different statistics are being considered for...

Three different statistics are being considered for estimating a population characteristic. The sampling distributions of the three statistics are shown in the following illustration:
Which of these statistics are unbiased estimators of the population characteristic?

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Key Concepts

Bias

Bias in an estimator is the difference between the expected value of the estimator and the actual value of the population parameter it attempts to estimate. An unbiased estimator is defined as one for which this difference is zero, meaning it hits the true parameter on average.

Population Parameter

A population parameter is a fixed, unknown numerical characteristic of a population, such as the mean or proportion, which researchers aim to estimate using sample data. The accuracy of estimators is often judged based on how well they recover this parameter on average.

Sampling Distribution

The sampling distribution is the probability distribution of a statistic obtained from a large number of samples drawn from the same population. It shows how the estimated values vary from sample to sample and is essential for understanding properties such as variability and bias in the estimator.

Unbiased Estimator

An unbiased estimator is a statistic used to estimate a population parameter, and it possesses the property that its expected value is equal to the true value of the parameter. This means that, over many samples, the estimator does not systematically overestimate or underestimate the parameter.

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