TYPES OF NUMERICAL DISTRIBUTIONS I. Characterizing numerical distributions. A. Unimodal and multi-modal distributions. B. Symmetrical and skewed distributions. C. Bell curves. II. Normal distributions. A. Characteristics. 1. Unimodal 2. Symmetrical. 3. Bell-shaped. B. The Empirical Rule. 1. 68% of all observations fall within one standard deviation of the mean. 2. 95% fall within two standard deviations of the mean. 3. 99% fall within three standard deviations of the mean. III. The standard normal distributions. A. Standardizing a normal distribution. 1. While all normal distributions are similar in shape, they can have different means and standard deviations. 2. However, every normal distribution can be converted to a standard normal distribution. a. Converting raw scores to z-scores (standard deviation units). b. Interpreting z-scores. B. Characteristics of the standard normal distribution. 1. Unimodal. 2. Symmetrical. 3. Bell-shaped. 4. Empirical Rule applies. 5. Mean of 0 and standard deviation of 1. C. The standard normal table. 1. What is the standard normal table? 2. Reading the standard normal table. 3. Proportion of a distribution above, below, and between scores. 4. Areas under the curve as probabilities.