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Density Curve

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.

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Density Curve

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  1. 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.

  2. 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.

  3. Mean and Median of Density Curves

  4. 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.

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

  6. 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.

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