Starnes, UPDATED The Practice of Statistics, 6e, Chapter 2

Percentile

The 𝑝th percentile of a distribution is the value with 𝑝% of observations less than or equal to it.

Cumulative relative frequency graph

Plots a point corresponding to the percentile of a given value in a distribution of quantitative data. Consecutive points are then connected with a line segment to form the graph.

Standardized score (z-score)

For an individual value in a distribution, tells us how many standard deviations from the mean the value falls, and in what direction.

Density curve

Models the distribution of a quantitative variable with a curve that: Is always on or above the horizontal axis; Has area exactly 1 underneath it. The area under the curve and above any interval of values on the horizontal axis estimates the proportion of all observations that fall in that interval.

Mean of a density curve

The point at which the curve would balance if made of solid material.

Median of a density curve

The equal-areas point, the point that divides the area under the curve in half.

Normal distribution

Described by a symmetric, single-peaked, bell-shaped density curve called a Normal curve.

Normal curve

Is completely specified by two parameters: its mean μ and standard deviation σ.

Empirical rule

The result in a Normal distribution with mean μ and standard deviation σ: Approximately 68% of the observations fall within σ of the mean μ.; Approximately 95% of the observations fall within 2σ of the mean μ.; Approximately 99.7% of the observations fall within 3σ of the mean μ.

standard Normal distribution

The Normal distribution with mean 0 and standard deviation 1.

Normal probability plot

A scatterplot of the ordered pair (data value, expected z-score) for each of the individuals in a quantitative data set. That is, the x-coordinate of each point is the actual data value and the y-coordinate is the expected z-score corresponding to the percentile of that data value in a standard Normal distribution.