Final answer:
The formula for common standard deviation is the square root of the mean squared error, meaning it is the square root of the variance, which can be calculated separately for populations and samples using different formulas.
Step-by-step explanation:
The formula for common standard deviation is the square root of the mean squared error, which in other terms is the square root of the variance. To calculate the variance, you need to find the mean of the squared deviations from the mean. For a population, this is done by summing the squared differences between each data point and the population mean (μ), and then dividing by the number of data points (N). For a sample, the squared differences are summed and then divided by the sample size minus one (n-1) to find the sample variance. Finally, the standard deviation is obtained by taking the square root of the variance.