The sample mean is the point estimator of which parameter?

The sample mean serves as the point estimator for the population mean because it provides the best estimate of the average value of the entire population based on the values observed in the sample. When a sample is collected, the sample mean calculates the average of that subset, and by the properties of sampling distributions, it is considered to be an unbiased estimator of the population mean. This means that as more samples are taken, the sample mean will tend to approach the actual population mean, making it a reliable measure for estimating the central tendency of a population.

In contrast, the sample size, population variance, and population proportion are distinct parameters that require different estimators. The sample size is simply a count of the observations in the sample and is not estimated from the data. The population variance estimates the degree of spread or dispersion around the mean within the entire population, typically estimated using the sample variance instead. Population proportion refers to the proportion of a particular characteristic in the population, which would be estimated using a different measure known as the sample proportion. Thus, the sample mean is specifically linked to estimating the population mean.