Is the sample mean a consistent estimator of the population mean? Explain

Sample Mean

The average of a subset of numbers from a larger set, representing the central tendency of that subset.

Consistent Estimator

An estimator that, as the sample size increases, converges in probability to the value of the parameter being estimated.

Population Mean

The average of all the values in a population.

Expatiate on the theories of consistency and relative efficiency as applied to estimators.
Comprehend the methodology for calculating an unbiased estimator of variance and mean.

Verified Answer

Final Answer :

Yes,the mean is consistent because it is unbiased and the standard error grows smaller as the sample size n increases.

Learning Objectives

Expatiate on the theories of consistency and relative efficiency as applied to estimators.
Comprehend the methodology for calculating an unbiased estimator of variance and mean.