VCE General Mathematics key terms

The arithmetic average found by adding all data values and dividing by how many values there are. It uses every observation, so extreme values can pull it noticeably up or down.

The middle value of an ordered data set. With an even number of values, it is the average of the two central values. It resists distortion by extreme observations.

The value or category that occurs most often in a data set. A set may have no mode, one mode, or several modes, and the mode works for categorical data too.

A measure of how far values typically spread from the mean. A small value means values cluster tightly; a large value means they are widely scattered.

The average of the squared distances of each value from the mean. Taking its square root gives the standard deviation, restoring the original units of measurement.

The difference between the upper and lower quartiles, covering the middle half of the data. It ignores the extreme quarters, so outliers do not affect it.

A value that divides ordered data into four groups of roughly equal size. The lower quartile has about one quarter of values below it; the upper quartile about three quarters.

An observation lying unusually far from the rest of the data. It may be a recording error or a genuine rare case, and it strongly affects the mean.

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

A chart for numerical data in which adjacent bars show the frequency of values in successive intervals. Bar heights or areas represent counts, revealing the shape of the distribution.

A table listing each value or class interval alongside how many times it occurs. Adding a relative frequency column gives proportions, and a cumulative column supports median and quartile work.

A running total of frequencies up to and including each class. Plotting it against the upper class boundary produces a curve from which medians and quartiles can be read.

The tendency of a distribution to stretch further on one side than the other. Positive skew has a long right tail with mean above median; negative skew is the reverse.

A number between negative one and positive one describing how closely paired data follow a straight line. Its sign gives direction; its size gives strength of linear association.

A straight line drawn through a scatterplot to summarise the trend in paired numerical data. It can be used to predict a response value from a given explanatory value.

A graph plotting one point per individual, using two numerical variables as coordinates. It displays the direction, strength and form of the relationship between them.

Using a fitted model to predict outside the range of observed data. Such predictions are risky because the relationship may change beyond the values actually measured.

A table cross-classifying individuals by two categorical variables, with counts in each cell. Row and column totals allow comparison of conditional percentages between groups.

A bar divided into sections whose lengths show the proportion of each category within a group. Placing bars side by side allows easy comparison of distributions across groups.

A number from zero to one expressing how likely an event is. Zero means impossible, one means certain, and the probabilities of all outcomes in a sample space sum to one.

The complete list or set of all possible outcomes of a random experiment. Listing it helps ensure every outcome is counted once when calculating probabilities.

The event that a given event does not happen. Its probability equals one minus the probability of the original event, which is often the quicker route to an answer.

Events that cannot both occur in the same trial. For such events, the probability that either happens equals the sum of their individual probabilities.

A situation where the occurrence of one event does not change the probability of another. For independent events, the probability that both occur equals the product of their probabilities.

The probability of an event given that another event is known to have occurred. It restricts attention to a reduced set of outcomes, often found from a two-way table.

A variable whose possible values are separate, countable numbers, each with an associated probability. Its probabilities must be non-negative and sum to one.

The long-run average of a random variable, found by multiplying each value by its probability and summing. It need not be a value the variable can actually take.

The probability model for the number of successes in a fixed number of independent trials, each with the same success probability. It applies only when those conditions hold.

Imitating a random situation many times, often with random numbers or technology, to estimate probabilities. More repetitions generally make the estimated probability more reliable.

A quantity or characteristic that can take different values across individuals or cases. In algebra it is usually represented by a letter standing for an unknown or changing number.

A combination of numbers, variables and operations without an equals sign. It can be simplified or evaluated but not solved, since it makes no claim of equality.

An equation in which each variable appears to the first power only, so its graph is a straight line. Solving it means finding the value or values making both sides equal.

Two or more equations that must be satisfied at the same time by the same unknowns. Their solution corresponds to the point where the graphs of the equations intersect.

Replacing a variable with a given number or expression to evaluate or simplify. In solving simultaneous equations it means inserting one equation's expression into the other.

Rules for combining powers with the same base, such as adding exponents when multiplying and subtracting them when dividing. They also cover zero, negative and fractional indices.

A root of a number that cannot be written as an exact fraction, such as the square root of two. Surds are often left in exact form rather than rounded decimals.

A rule assigning exactly one output to each permitted input. Its graph therefore passes the vertical line test, and each input has only one corresponding value.

The domain is the set of all permitted input values of a function; the range is the set of all resulting output values. Both may be restricted by context or by the rule itself.

A measure of how steeply a line rises or falls, calculated as the change in the vertical value divided by the change in the horizontal value between two points. It gives the rate of change.

A function that reverses another, sending each output back to its original input. Its graph is the reflection of the original in the line where both coordinates are equal.

A line that a curve approaches ever more closely without necessarily meeting. Exponential graphs typically have a horizontal asymptote, indicating a limiting value.

A function in which the variable appears in the exponent, producing repeated multiplication. It models growth or decay at a constant percentage rate per unit of time.

The total distance around the boundary of a two-dimensional shape. For circles it is called the circumference and is found from the radius using pi.

The amount of surface enclosed by a two-dimensional shape, measured in square units. Formulas differ by shape, and composite figures are split into simpler parts.

The amount of three-dimensional space occupied by a solid, measured in cubic units. For prisms and cylinders it equals the cross-sectional area multiplied by the length or height.

The total area of all outer faces of a three-dimensional object, measured in square units. For curved solids it combines flat faces with curved sections such as the side of a cylinder.

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 and distances.

A ratio of two sides of a right-angled triangle linked to an acute angle, namely sine, cosine or tangent. These ratios allow unknown sides and angles to be calculated.

Shapes with identical angles whose corresponding side lengths are in a constant ratio. Their areas compare as the square of that ratio and volumes as its cube.

The multiplier relating corresponding lengths in similar figures or in a scale drawing. Lengths, areas and volumes scale by its first, second and third powers respectively.