Glossary
Binomial Distribution
A discrete probability distribution used for a fixed number of independent trials, where each trial has only two possible outcomes (success/failure) and the probability of success is constant.
Example:
Calculating the probability of getting exactly 7 heads in 10 coin flips uses the binomial distribution.
Categorical Variables
Variables that place individuals into distinct categories, often displayed in frequency tables or two-way tables.
Example:
A survey question asking about a person's favorite type of pet (e.g., dog, cat, bird) collects data on a categorical variable.
Density Curves
A curve that is always on or above the horizontal axis and has a total area of exactly 1 underneath it, representing the probability distribution of a continuous random variable.
Example:
The smooth, bell-shaped curve representing the distribution of human heights is a density curve.
Dependent Events
Events where the outcome of one event influences or changes the probability of another event occurring.
Example:
Drawing two cards from a deck without replacement means the probability of the second card is dependent on the first card drawn.
Geometric Distribution
A discrete probability distribution that models the number of independent trials required to achieve the first success.
Example:
Determining the probability that it takes exactly 5 attempts to make your first free throw in basketball is an application of the geometric distribution.
Independence
A condition where the outcome of one event does not affect the probability of another event occurring.
Example:
When rolling a die twice, the result of the first roll and the result of the second roll are independent events.
Mutually Exclusive
Events that cannot happen at the same time; if one event occurs, the other cannot.
Example:
When drawing a single card from a deck, the events 'drawing a King' and 'drawing an Ace' are mutually exclusive.
Normal Distribution
A symmetrical, bell-shaped continuous probability distribution characterized by its mean (μ) and standard deviation (σ), widely used to model many natural phenomena.
Example:
The scores on a standardized test for a large population often follow a normal distribution.
Probability
The chance or likelihood of an event occurring, quantified as a value between 0 and 1 (or 0% and 100%).
Example:
The probability of drawing a red card from a standard deck of 52 cards is 26/52 or 0.5.
Probability Distributions
A description of the possible values a random variable can take and the likelihood (probability) associated with each of those values.
Example:
A table listing the number of heads (0, 1, 2, 3) and their probabilities when flipping three coins shows a probability distribution.
Quantitative Variables
Variables that take numerical values for which arithmetic operations like adding or averaging make sense, often modeled by density curves.
Example:
The amount of rainfall in inches recorded in a city each month is a quantitative variable.
Random Variables
Variables whose values are numerical outcomes of random phenomena, meaning their values are determined by chance.
Example:
If you count the number of times a specific song plays on a shuffled playlist, that count is a random variable.
Z-Scores
A standardized measure that indicates how many standard deviations a particular data point is away from the mean of its distribution.
Example:
If a student's test score has a z-score of 2, it means their score is two standard deviations above the class average.