Question

Explain the difference between \(\sigma\) and \(\sigma_{\bar{x}}\) and between \(\mu\) and \(\mu_{\bar{x}}\)

Short answer

σ is the standard deviation of a population and μ is the mean of the population. σ_{\bar{x}} is the standard deviation of the sample means, also known as the standard error, and μ_{\bar{x}} is the average of the sample means from the population. Hence, 'σ' and 'μ' pertains to the entire population while 'σ_{\bar{x}}' and 'μ_{\bar{x}}' pertain to statistical samples taken from the population.

Step-by-step solution

Understanding σ and σ_{\bar{x}}

The symbol σ stands for the population standard deviation, it quantifies the amount of variation in a set of data values. While σ_{\bar{x}}, also known as the standard error, represents the standard deviation of the distribution of the sample means. It quantifies the precision with which the mean of a sample estimates the mean of the population.

Understanding μ and μ_{\bar{x}}

The symbol μ is used to represent the population mean, which is the average of all values in the population. On the other hand, μ_{\bar{x}} is the mean of the sample means, that signifies the average of all the sample means from the population.