AP STATS UNIT 2 VOCAB

Tchebysheff’s Theorem

Given a list of data L1 = x , x , x …… and k a real number greater than 0, then at least 1- [1/(k^2)] of the observations lie within k standard deviations of the mean.

Central Area

The area under a density curve and above the x-axis, bounded above and below, and is symmetric about the mean.

Critical Value

A domain value either x or z , that captures a fixed area beneath a density curve. The superscript “star” designates such a value.

Density Curves, Axiom 1

A density curves always lie on or above the x-axis.

Density Curves, Axiom 2

The total area under a density curve is equal to 1.

Density Curves, Axiom 3

A density curve is a complete description of the overall pattern.

Density Curves, Axiom 4

The area under a density curve and above the x-axis, bounded below and above, equals the probability of a randomly selected observation landing in that interval

The Empirical Rule

States that a distribution is approximately Normal if and only if…

Empirical Rule I

approximately 68% of the data are contained inside

Empirical Rule II

approximately 95% of the data are contained inside

Empirical Rule III

approximately 99.7% of the data are contained inside

Z-Score

The standardized value in the Z-domain giving distance from the mean, and associated with the corresponding X-domain given in the problem (usually from a sample).