Estimator
Estimator is a formula applied to sample data to approximate an unknown population parameter. The sample mean is the standard estimator of the true population mean.
See it move
The flow diagram traces the path from a population containing the unknown true parameter θ, to a sample of n observations drawn from it, through the estimator rule x̄ = Σxᵢ ÷ n, to a numerical estimate θ̂ that approximates θ. The three connectors — draw from, apply, produces — label each transition and make explicit the distinction between the general formula (the estimator) and the single number it outputs for any one particular sample (the estimate).
The formula
Variables
- Sample mean — the canonical estimator of the population mean μ
- Sample size
- Individual observation i
Unbiased: E[x̄] = μ; as n grows, x̄ converges in probability to μ (consistency)
Check yourself
Two researchers estimate the same population mean from the same dataset. Researcher A uses the sample mean x̄; Researcher B uses (x̄ + 5). Which comparison is correct?