Functions, Relations, and Measures of Central Tendency and Dispersion

Vocabulary flashcards covering mathematical functions, relations, domain and range, measures of central tendency, and grouped/ungrouped data variance and standard deviation.

Function

A relation defined as a set of ordered pairs $(x, y)$ where no two or more distinct ordered pairs have the same first element ($x$).

Relation

A rule that relates values called the domain to a second set of values called the range.

Injective Function

Another technical term for a one-to-one function.

Surjective Function

Another technical term for an onto function.

Ways to Describe a Function

The five representations used to express a function: ordered pairs, table of values, mapping diagrams, graphs, and function equations.

Domain

The set of all $x$-inputs in a relation or function.

Range

The set of all $y$-outputs in a relation or function.

Evaluating a Function

The algebraic procedure of replacing the variable in a function with a specific numeric value or expression.

Measure of Central Tendency

In layman's terms, a statistical measure that represents the average of a data set.

Mean

The arithmetic average of a data set, denoted by $\mu$ (read as "mu") for population data or $\bar{x}$ (read as "x-bar") for sample data.

Median

The middle value of an ordered data set arranged in ascending or descending order, denoted by $\tilde{x}$ ("x-tilde").

Mode

The value that appears most frequently in a data set, denoted by $\hat{x}$ ("x-hat").

Unimodal

A data distribution having only one mode (one repeating most frequent number).

Bimodal

A data distribution containing two distinct modes or two values that share the highest frequency.

Multimodal

A data distribution having multiple modes (more than two values repeating with equal highest frequency).

Mean for Grouped Data Formula

The formula $\bar{x} = \frac{\sum fx}{N}$, where $f$ represents frequency, $x$ is the class mark, and $N$ is the total frequency.

Class Mark ($x$)

The middle value or midpoint of a score interval in grouped frequency distribution data.

Class Boundaries

Values calculated for a score interval by subtracting $0.5$ from the lower score limit and adding $0.5$ to the upper score limit (e.g., $46-50$ becomes $45.5-50.5$).

Sample Variance for Ungrouped Data

The measure of dispersion calculated using $s^2 = \frac{\sum (x - \bar{x})^2}{n - 1}$, where each score deviation from the mean is squared and summed, then divided by $n - 1$.

Sample Variance for Grouped Data Formula

The formula $s^2 = \frac{\sum f(x - \bar{x})^2}{n - 1}$, used to calculate the variance of grouped data using class marks $x$, frequencies $f$, and the sample mean $\bar{x}$.