VCE Foundation Mathematics key terms

The average found by adding all the values in a data set and dividing that total by the number of values. It is affected strongly by unusually large or small values.

The middle value of a data set once all values are arranged in order. If there is an even number of values, it is the average of the two middle values.

The value or values that occur most often in a data set. A data set may have no mode or several modes, and the mode can be used for non-numerical categories.

A simple measure of spread found by subtracting the smallest value from the largest value in a data set. It depends on only two values and ignores the rest.

The spread of the middle half of a data set, calculated as the upper quartile minus the lower quartile. It is not affected by extreme values at either end.

One of three values that split an ordered data set into four groups of roughly equal size. The lower, middle and upper quartiles are often labelled Q1, Q2 and Q3.

A value that lies far away from the main cluster of a data set. Outliers can distort the mean and range, so they are often identified and discussed separately.

A table that lists each category or value alongside the number of times it occurs. It can also include relative frequencies or cumulative totals to summarise a data set compactly.

A graph for numerical data in which touching bars show the frequency of values within equal class intervals. The horizontal axis is continuous and bar heights represent counts or relative frequencies.

A display that splits each data value into a leading stem and a final leaf digit, keeping every value visible while showing shape. Ordered leaves make medians and quartiles easy to locate.

A diagram showing the minimum, lower quartile, median, upper quartile and maximum of a data set. The box covers the middle half of the data and whiskers extend to the extremes.

A graph plotting one numerical variable against another as individual points. It is used to look for patterns, trends, clusters and unusual points between two variables.

A description of the strength and direction of a straight-line relationship between two numerical variables. It may be positive, negative or close to zero, and is not proof of cause.

A straight line drawn through a scatterplot to summarise the overall trend of the points. It can be used to make predictions, with caution outside the observed data range.

Data that records which group or category each item belongs to, such as eye colour or transport method. Categories may be named or ordered, and counts are summarised with frequencies.

Data recorded as numbers that represent a quantity, such as height, age or cost. It may be discrete, taking separate values, or continuous, taking any value in a range.

A number between 0 and 1 describing how likely an event is, where 0 means impossible and 1 means certain. It can be estimated from experiments or calculated from equally likely outcomes.

The complete list or diagram of all possible outcomes of a chance experiment. Listing it carefully helps ensure probabilities are calculated from every equally likely outcome.

The event that does not occur when a given event does not happen, with probability equal to one minus the probability of the event. Together the two events cover all outcomes.

Two events that cannot both happen at the same time, such as rolling a 2 and rolling a 5 on one die. Their combined probability is the sum of their separate probabilities.

Two events where the occurrence of one does not change the probability of the other, such as separate coin tosses. Their joint probability is found by multiplying the individual probabilities.

A branching diagram showing the possible outcomes of a multi-stage experiment. Probabilities are written on branches and multiplied along paths to find combined outcomes.

A table that cross-classifies items by two categorical variables, with totals for each row and column. It supports calculations of probabilities from counts in surveys and experiments.

The proportion of trials in which an event occurred, found by dividing the number of successes by the total number of trials. With many trials it tends to approach the theoretical probability.

A letter or symbol that stands for a value that can change or is not yet known. Expressions, equations and formulas are built from variables combined with numbers and operations.

A combination of numbers, variables and operations without an equals sign, such as 3x + 5. An expression can be simplified or evaluated but not solved.

A statement that two expressions are equal, containing an equals sign and usually an unknown to be found. Solving it means finding values that make the statement true.

Terms that contain exactly the same variable parts, such as 4x and 7x, and so can be added or subtracted together. Collecting them simplifies an expression without changing its value.

The number multiplying a variable in a term, such as the 6 in 6y. A coefficient of 1 is usually not written, and a negative sign belongs to the coefficient.

A rule written as an equation linking quantities, such as area equals length times width. Substituting known values into a formula allows the remaining quantity to be calculated.

Replacing variables in an expression or formula with given numbers and then calculating the result. Correct order of operations matters when the expression contains several operations.

A relationship whose graph is a straight line, showing a constant rate of change. It can be described by an equation of the form y equals mx plus c.

A measure of how steeply a line rises or falls, found by dividing vertical change by horizontal change between two points. A positive gradient rises to the right, a negative one falls.

The point where a graph crosses the vertical axis, occurring where the horizontal variable equals zero. In a linear rule it is the constant term c.

The U-shaped curve produced by a quadratic relationship. It has a turning point that is a minimum when the curve opens upward and a maximum when it opens downward.

A vertical line through the turning point of a parabola that divides the curve into two mirror-image halves. Points equally distant either side of it share the same output value.

The total distance around the outside of a two-dimensional shape, found by adding the lengths of all its sides. For a circle the special name for this distance is the circumference.

The amount of flat surface covered by a two-dimensional shape, measured in square units. Each shape has its own rule, such as length times width for a rectangle.

The amount of three-dimensional space occupied by a solid, measured in cubic units. For prisms it is found by multiplying the cross-sectional area by the object's length or height.

The distance around the edge of a circle, calculated as pi multiplied by the diameter. It is the circle's version of perimeter and is measured in ordinary length units.

A rule stating that in a right-angled triangle the square of the hypotenuse equals the sum of the squares of the other two sides. It is used to find unknown side lengths.

Shapes with the same shape but possibly different sizes, having equal matching angles and proportional matching sides. Lengths scale by one factor while areas scale by its square.

The multiplier that compares corresponding lengths in two similar figures or on a scale drawing. It converts measurements between the drawing and the real object.

The total area of all the outer faces of a three-dimensional object, measured in square units. It is found by calculating the area of each face and adding them together.