Year 9 Mathematics: Statistics, Probability, and Algebra

Essential vocabulary flashcards covering Year 9 statistics, data displays, probability concepts, like and unlike terms, and algebraic substitution.

Statistics

The study of data, including ways to gather, review, analyse, and draw conclusions from data.

Variable

A symbol or characteristic used to denote and record characteristics of individuals or things.

Univariate Data

A type of statistical investigation or data set that involves or deals with only $1$ variable.

Bivariate Data

Statistical data that involves $2$ variables to explore or determine the relationship between them.

Discrete Data

Data that can only take certain values, can be counted, has a limited number of values, and usually comes in the form of whole numbers or integers.

Continuous Data

Data that refers to measurements with values that are not fixed, have an infinite number of possible values, and can be broken down into smaller individual parts.

Statistical Enquiry Cycle

The five-step cycle for conducting a statistical investigation: Problem, Plan, Data, Analysis, and Conclusion.

Line Graph

A graphical representation commonly drawn to show information that changes over a period of time by joining plotted points with straight line segments across an $x$-axis and $y$-axis.

Bar Graph

A graphical representation of data, quantities, or numbers using bars or strips used to compare and contrast distinct categories or frequencies.

Pictograph

A picture graph that uses symbols and pictures along with a defined key to represent quantities in a data set.

Pie Chart

A circular pictorial graph where the whole circle represents the entire data set and slices represent the relative proportions or parts of the whole.

Dot Plot

A visual method of representing data series by stacking dots horizontally or vertically to group points based on the value of each point.

Scatter Plot

A graph showing the relationship between two quantitative variables measured for the same individuals, with one variable on the horizontal axis and the other on the vertical axis.

Histogram

A graph similar to a bar chart that groups continuous numerical data into ranges, where the height of each bar shows how many values fall into each range.

Box Plot

A graph (also known as a box and whisker plot) summarizing a set of data using five key values: lowest value, lower quartile ($Q_1$), median ($M$), upper quartile ($Q_3$), and highest value.

Lower Quartile ($Q_1$)

The first quartile or value below which $25\%$ of ordered data values lie.

Upper Quartile ($Q_3$)

The third quartile or value below which $75\%$ of ordered data values lie (with the remaining $25\%$ lying above it).

Interquartile Range ($\text{IQR}$)

The spread of the middle $50\%$ of a data set, calculated as the upper quartile minus the lower quartile ($\text{IQR} = Q_3 - Q_1$).

Mean

The arithmetic average of a data set, calculated by adding up all numbers in the set and dividing by the total number of values.

Median

The middle value or midpoint when a data set is ordered from least to greatest.

Mode

The value or values that appear the most number of times in a set of data.

Range

The difference between the largest (highest) value and the smallest (lowest) value in a data set.

Probability Scale

A continuous scale from $0$ to $1$ (or $0\%$ to $100\%$) used to measure chance, with benchmarks including Impossible ($0$), Even Chance ($0.5$), and Certain ($1$).

Probability of an Outcome ($P(\text{outcome})$)

The likelihood of a specific event occurring, defined as $\frac{\text{number of ways the outcome can happen}}{\text{total number of possible outcomes}}$.

Like Terms

Algebraic terms that have the exact same variable letters raised to the exact same powers (e.g., $10x$ and $5x$, or $abc$ and $cba$).

Unlike Terms

Algebraic terms that have different variables or variables raised to different powers (e.g., $3y$ and $6x$, or $2x^2y$ and $2xy^2$).

Collecting Like Terms

The algebraic procedure of simplifying an expression by adding or subtracting the coefficients of terms containing identical variables.

Substitution

The algebraic process of replacing letters or variables with given numbers to calculate the numerical value of an expression.

Order of Operations in Algebra

The mathematical convention dictating that expressions within brackets are evaluated first, followed by multiplication and division, and lastly addition and subtraction.

Algebraic Fraction Line

A horizontal division bar indicating that the entire numerator is divided by the denominator, acting as grouping brackets for the top expression.