Glossary
Center
A measure that describes the typical or central value of a distribution, often represented by the mean or median.
Example:
The average score on a challenging AP Statistics exam would represent the center of the score distribution.
Continuous Random Variable
A type of random variable that can take on any value within a given range, typically obtained by measuring.
Example:
The exact amount of time it takes for a student to complete an AP Statistics free-response question is a continuous random variable.
Discrete Random Variable
A type of random variable that can only take on a finite or countably infinite number of distinct values, typically obtained by counting.
Example:
The number of red cars that pass a specific intersection in an hour is a discrete random variable.
Double-Peaked
A distribution characterized by two distinct high points or modes, suggesting two different groups or clusters within the data.
Example:
A histogram of commute times for employees might be double-peaked if some employees live very close to work and others live very far, with fewer in between.
Left-Skewed
A distribution where the tail extends further to the left, meaning most values are concentrated on the right side and there are a few smaller values.
Example:
The distribution of scores on an easy exam might be left-skewed, with most students scoring high and only a few scoring low.
Peaks
The high points in a distribution's graph, indicating where values are most concentrated or frequent.
Example:
If a survey on favorite music genres showed two distinct groups (e.g., pop and classical), the distribution might have two peaks.
Probability Distribution
A description that tells you the probability of each possible value a random variable can take. The sum of all probabilities in a distribution always equals 1.0.
Example:
A table showing the likelihood of rolling each number (1 through 6) on a fair die represents its probability distribution.
Random Variable
A variable whose value is a numerical outcome of a random phenomenon. It acts as a placeholder for the results of a chance event.
Example:
When you flip a coin three times, the number of heads you get (0, 1, 2, or 3) is a random variable.
Right-Skewed
A distribution where the tail extends further to the right, meaning most values are concentrated on the left side and there are a few larger values.
Example:
The distribution of the number of times a person has visited a specific theme park is often right-skewed, as most people visit rarely, but a few visit very often.
Single-Peaked
A distribution characterized by one dominant high point or mode, indicating a single concentration of values.
Example:
The distribution of heights for adult females typically appears single-peaked around the average height.
Skewness
A measure of the asymmetry of a distribution, indicating if the tail of the distribution is longer on one side than the other.
Example:
The distribution of household income in a country often exhibits skewness to the right, with a long tail of high earners.
Symmetry
A characteristic of a distribution where values are evenly distributed around the center, often resembling a mirror image on either side.
Example:
A histogram of the heights of all adult humans would likely show symmetry around the average height.
Variability
A measure that describes the spread or dispersion of the values in a distribution, often represented by the standard deviation or range.
Example:
If all students in a class scored very similarly on a quiz, the variability of their scores would be low.