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.