• The overall pattern of a distribution can often be described compactly by a

**density curve**. A density curve has total area 1 underneath it. Areas under a density curve give proportions of observations for the distribution.• The

**mean***μ*(balance point), the**median**(equal-areas point), and the**quartiles**can be approximately located by eye on a density curve. The**standard deviation***σ*cannot be located by eye on most density curves. The mean and median are equal for symmetric density curves, but the mean of a skewed curve is located farther toward the long tail than is the median.• The

**Normal distributions**are described by bell-shaped, symmetric, unimodal density curves. The mean*μ*and standard deviation*σ*completely specify the Normal distribution*N*(*μ*,*σ*). The mean is the center of symmetry, and σ is the distance from μ to the change-of-curvature points on either side. All Normal distributions satisfy the**68–95–99.7 rule**.70

• To

**standardize**any observation*x*, subtract the mean of the distribution and then divide by the standard deviation. The resulting*z*-score*z*= (*x*−*μ*)/*σ*says how many standard deviations*x*lies from the distribution mean. All Normal distributions are the same when measurements are transformed to the standardized scale.• If

*X*has the*N*(*μ*,*σ*) distribution, then the standardized variable*Z*= (*X*−*μ*)/*σ*has the**standard Normal distribution***N*(0, 1). Proportions for any Normal distribution can be calculated by software or from the**standard Normal table**(Table A), which gives the**cumulative proportions**of*Z*<*z*for many values of*z*.• The adequacy of a Normal model for describing a distribution of data is best assessed by a

**Normal quantile plot**, which is available in most statistical software packages. A pattern on such a plot that deviates substantially from a straight line indicates that the data are not Normal.