Density Curve A mathematical model for data, providing a way to describe an entire distribution with a single mathematical expression. An idealized description of the data distribution, representing perhaps the population from which we obtained our sample.

Properties of a Density Curve Always on or above the horizontal axis. The total area under the curve is exactly 1. The area under the curve for a given horizontal range is the relative frequency of observations in that range for the idealized (population) distribution.

Mean and Median of Density Curves

m and s The mean of a density curve is denoted by the Greek letter m. The standard deviation of a density curve is denoted by the Greek letter s.

Normal Distributions Symmetric Single-peaked (i.e., unimodal) Bell-shaped Exact form for a particular normal distribution is specified by m and s.

The 68-95-99.7 Rule In any normal distribution: 68 % of the individuals fall within 1s of m. 95 % of the individuals fall within 2s of m. 99.7 % of the individuals fall within 3s of m.