Question

What is the difference between \(\bar{x}\) and \(\mu\) ? between \(s\) and \(\sigma\) ?

Short answer

\(\bar{x}\) is the sample mean and \(\mu\) is the population mean - avg. of a sample data set Vs the avg. of an entire population. \(s\) is sample standard deviation and \(\sigma\) is the population standard deviation, measure of the spread of sample data points around the sample mean Vs measure of spread of all data points around the population mean.

Step-by-step solution

Understand Sample Mean and Population Mean

\(\bar{x}\) represents the 'sample mean', which is the average of a set of observations drawn from a larger population. The formula to calculate \(\bar{x}\) is \(\bar{x} = \frac{1}{n}\sum_{i=1}^{n} x_i\), where \(x_i\) are the data points and \(n\) is the number of data points. \(\mu\) represents the 'population mean', which is the average of the entire population. The formula to calculate \(\mu\) is \(\mu = \frac{1}{N}\sum_{i=1}^{N} x_i\), where \(N\) is the total number of the population.

Understand Sample Standard Deviation and Population Standard Deviation

\(s\) represents the 'sample standard deviation', which describes the spread of data points around the sample mean in a set of observations from a population. The formula to calculate \(s\) is \(s = \sqrt{\frac{1}{n-1}\sum_{i=1}^{n} (x_i - \bar{x})^2}\), where \(\bar{x}\) is the sample mean. \(\sigma\) represents the 'population standard deviation', which describes the spread of data points around the population mean in the entire population. The formula to calculate \(\sigma\) is \(\sigma = \sqrt{\frac{1}{N}\sum_{i=1}^{N} (x_i - \mu)^2}\), where \(\mu\) is the population mean.