Chapter 2 Vocab Quiz List

Percentile

The pth percentile is the value such that p% of the observations are less than or equal to that value.

Median

The middle value of an ordered distribution; the 50th percentile.

First Quartile (Q₁)

The value with approximately 25% of the observations at or below it.

Third Quartile (Q₃)

The value with approximately 75% of the observations at or below it.

Cumulative Frequency

The total number of observations that are less than or equal to a particular value.

Relative Frequency

The proportion or percentage of observations in a particular category or interval.

Cumulative Relative Frequency

The proportion or percentage of observations that are less than or equal to a particular value.

Cumulative Relative Frequency Graph

A graph showing the cumulative percentage or proportion of observations less than or equal to different values.

Ogive

Another name for a cumulative relative frequency graph.

Standardized Score

A value that describes how many standard deviations an observation is from the mean.

z-Score

A standardized score that measures how many standard deviations an observation is above or below the mean.

Positive z-Score

A z-score greater than 0, indicating that an observation is above the mean.

Negative z-Score

A z-score less than 0, indicating that an observation is below the mean.

Transformation

A mathematical change applied to every observation in a data set.

Center

A measure describing the typical or central value of a distribution, such as the mean or median.

Variability

The amount of spread or dispersion in a distribution.

Range

The difference between the maximum and minimum values in a data set.

Interquartile Range (IQR)

The difference between the third quartile and first quartile; IQR = Q₃ − Q₁.

Standard Deviation

A measure of the typical distance that observations are from the mean.

Density Curve

An idealized curve used to model the overall pattern of a distribution; it is always on or above the horizontal axis and has a total area of 1 underneath it.

Area Under a Density Curve

The proportion or percentage of observations represented by a section of the distribution.

Mean of a Density Curve

The balance point of the density curve.

Median of a Density Curve

The point that divides the area under the density curve into two equal halves.

Parameter

A number that describes a characteristic of a population or probability distribution.

Normal Distribution

A symmetric, single-peaked, bell-shaped distribution described by its mean and standard deviation.

Normal Curve

The bell-shaped density curve associated with a Normal distribution.

μ (Mu)

The symbol used to represent the mean of a population or Normal distribution.

σ (Sigma)

The symbol used to represent the standard deviation of a population or Normal distribution.

Empirical Rule

The rule stating that approximately 68%, 95%, and 99.7% of observations in a Normal distribution are within 1, 2, and 3 standard deviations of the mean, respectively.

68–95–99.7 Rule

Another name for the Empirical Rule.

Standard Normal Distribution

A Normal distribution with a mean of 0 and a standard deviation of 1.

Standardizing

Converting an observation into a z-score.

Unstandardizing

Converting a z-score back into an original value.

Area to the Left

The proportion or probability of observations below a particular value or z-score.

Area to the Right

The proportion or probability of observations above a particular value or z-score.

Area Between

The proportion or probability of observations that fall between two values.

Normal Probability Plot

A graph used to assess whether a distribution is approximately Normal by examining whether the plotted points follow an approximately straight line.

Normal Quantile Plot

Another name for a Normal probability plot.

Approximately Normal

A description used when real-world data reasonably follow the general shape and properties of a Normal distribution.

Symmetric Distribution

A distribution whose left and right sides are approximately mirror images of each other.

Skewed Right

A distribution with a longer tail extending to the right; the mean is generally greater than the median.

Skewed Left

A distribution with a longer tail extending to the left; the mean is generally less than the median.

Unimodal

Having one major peak.

Mean

A measure of center calculated by averaging all observations.

Standard Deviation from the Mean

A measure of how far a value is from the mean expressed in units of standard deviation.

Key Formula — z-Score

z = (x − μ) / σ

Key Formula — Unstandardizing

x = μ + zσ

Key Formula — IQR

IQR = Q₃ − Q₁

Key Rule — Adding/Subtracting a Constant

Adding or subtracting a constant changes measures of center and location but does not change the distribution's variability or shape.

Key Rule — Multiplying/Dividing by a Positive Constant

Multiplying or dividing every observation by a positive constant changes measures of center, location, and variability by that factor but does not change the shape.