Illuminating Statistical Analysis Using Scenarios and Simulations

CStandard Error as Standard Deviation

Variance and its square root, standard deviation, are general-purpose statistics for distributions, be it distributions of sample data or distributions of sample statistics. Below are the formulas for the variance and standard deviation of sample data values around the population mean, where is the number of data values, is the sample data value, and is the population mean.

Next, let's look at the normal distribution that results from a sampling simulation of sample means for 10,000 random samples of size 100—see Figure C.1. The population mean is 10 and the population variance is 4.

Figure C.1

Below are the analogous formulas for the variance ...