The Mean, Standard Deviation, and Sampling Distribution of the Sample Mean
The Mean and Standard Deviation of the Sample Mean
Key Takeaways
- The sample mean is a random variable; as such it is written \(\bar{X}\), and \(\bar{x}\) stands for individual values it takes.
- As a random variable the sample mean has a probability distribution, a mean \(\mu_{\bar{X}}\), and a standard deviation \(\sigma_{\bar{X}}\).
- There are formulas that relate the mean and standard deviation of the sample mean to the mean and standard deviation of the population from which the sample is drawn.