The sample mean $ẏ$ is the point estimator of which population parameter?

• A. The population median $\mathrm{Me}$
• B. The population mean $\mu$
• C. The population variance ${\sigma }^2$
• D. The population mode $\mathrm{Mo}$

Answer: (B)

Verified step by step guidance

1. Understand that a point estimator is a statistic used to estimate a specific population parameter based on sample data.
2. Recall that the sample mean, often denoted as \(\bar{x}\), is calculated by summing all sample observations and dividing by the sample size \(n\): \(\bar{x} = \frac{1}{n} \sum_{i=1}^n x_i\).
3. Recognize that the sample mean is used to estimate the population mean, which is the average value of the entire population, denoted by \(\mu\).
4. Note that other population parameters like the median, variance, and mode have different estimators (e.g., sample median, sample variance, sample mode).
5. Therefore, the sample mean serves as the point estimator specifically for the population mean.