Properties of Gaussian Curves

Figure 1.1 shows two Gaussian curves in which we plot the relative frequency y of various deviations from the mean versus the deviation from the mean.

Figure 1.1 Normal error curves. The standard deviation for curve B is twice that for curve A, that  is, σ_B = ₂σ_A. In (a) the abscissa is the deviation from the mean (x – m) in the units of measurement.

As shown in curves such as these can be described by an equation that contains just two parameters, the population mean μ and the population standard deviation σ.

The term parameter refers to quantities such as μ and σ that define a population or distribution. Data values such as x are variables. The term statistic refers to an estimate of a parameter that is made from a sample of data as discussed below. The sample mean and the sample standard deviation are examples of statistics that estimate parameters m and s respectively.