Introduction to Probability and Descriptive Statistics Review

Vocabulary flashcards covering foundational probability concepts, experimental terminology, counting principles, and review of data variation from the lecture.

Deviation

The measure of how much an individual data point deviates from the mean.

Variance

The sum of the squared deviations from the mean, calculated by dividing by $n - 1$ for a sample or by big $N$ for a population.

Standard Deviation

The square root of the variance, represented by the notation $\sigma$ for a population and $s$ for a sample.

Coefficient of Variation

The standard deviation divided by the mean, used primarily to compare the variation of variables measured on different scales (such as weight versus height).

Empirical Rule

A rule for bell-shaped distributions stating that approximately $68\%$ of data falls within one standard deviation of the mean, $65\%$ falls within two standard deviations, and $99.7\%$ falls within three standard deviations.

Chebyshev's Theorem

A rule applying to any distribution stating that at least $1 - \frac{1}{k^2}$ of the data lies within $k$ standard deviations of the mean, resulting in at least $75\%$ within two standard deviations and about $88\%$ within three standard deviations.

Outlier

A data point considered extreme because it lies at least $3$ standard deviations away from the mean or beyond $1.5 \times \text{IQR}$ ($1.5$ quartile).

Probability

The likelihood of an event to occur, or long-term relative frequency, which assigns a numerical value bounded strictly between $0$ and $1$ to quantify uncertainty.

Probability Experiment

An action or trial through which specific results, such as counts, measurements, or responses, are obtained.

Sample Space

The set of all possible outcomes of a probability experiment.

Outcome

The specific result of a single trial in a probability experiment.

Event

A subset of all possible outcomes in a sample space, consisting of a single outcome or multiple outcomes.

Theoretical Probability

The probability calculated as the ratio of the number of outcomes within an event $E$ to the total number of possible outcomes in the sample space.

Empirical Probability

The probability derived from observation or relative frequency, calculated as the observed frequency of an event divided by the total frequency of experimental trials.

Law of Large Numbers

The principle stating that as an empirical experiment is repeated over and over for a large number of trials, the empirical probability ($\hat{P}$) converges toward the theoretical probability ($P$).

Fundamental Counting Principle

A method to determine the total number of possible outcomes across a sequence of experiments, where an experiment with $m$ outcomes followed by an experiment with $n$ outcomes yields $m \times n$ total possible outcomes.

Complement of an Event

The set of all outcomes in a sample space that are not included in a given event $E$, denoted as $E'$, with a probability equal to $1 - P(E)$.

Mutually Exclusive Events

Events that cannot happen at the same time because there is no overlapping outcome that satisfies both event criteria simultaneously.