Free VCE General Mathematics Flashcard Review

Categorical: labels/groups — nominal (no order, e.g. suburb) or ordinal (ordered, e.g. star rating). Numerical: counts/measurements — discrete (counted, e.g. number of siblings) or continuous (measured, e.g. height).

IQR = Q3 − Q1. A value is an outlier if it is below Q1 − 1.5×IQR or above Q3 + 1.5×IQR. Whiskers end at the most extreme data values still inside the fences.

When the distribution is skewed or contains outliers — median and IQR are resistant, while the mean and SD are dragged toward the tail/outliers. Use mean and SD only for roughly symmetric data with no outliers.

In a normal distribution, about 68% of values lie within 1 SD of the mean, 95% within 2 SDs, and 99.7% within 3 SDs. Use symmetry to get tail percentages, e.g. 16% lie more than 1 SD above the mean.

z = (value − mean) ÷ SD. Gives the number of standard deviations a value sits above (+) or below (−) the mean, allowing comparison of values from different distributions.

State direction (positive/negative), form (linear/non-linear) and strength (strong/moderate/weak). The explanatory variable (EV) goes on the horizontal axis; the response variable (RV) on the vertical axis.

Template: 'r²×100% of the variation in the [RV] is explained by the variation in the [EV].' E.g. r² = 0.64 → 64% explained, the remaining 36% by other factors. Note r² is the square of r.

A strong association between EV and RV does not show the EV causes the RV. Other explanations: a confounding (lurking) variable influencing both, a common response, or coincidence. Causation requires a controlled experiment.

Equation: y = a + bx. Slope b = r × (SD of y ÷ SD of x); intercept a = (mean of y) − b × (mean of x). Valid only for two numerical variables with a linear form.

Template: 'On average, the [RV] increases (b positive) / decreases (b negative) by |b| [units] for each one-[unit] increase in the [EV].' Always include 'on average' and the actual variable names.

Residual = actual value − predicted value (from the line). A residual plot with random scatter about zero supports a linear model; a clear curve or pattern means linearity is not appropriate.

Interpolation: predicting within the range of the original data — reasonably reliable. Extrapolation: predicting outside that range — unreliable, since there is no evidence the linear trend continues beyond the data.

Replace each value with the mean of itself and its neighbours (3-point: previous + itself + next, ÷ 3) to reduce random fluctuation. Trap: an even-point moving mean (e.g. 4-point) must then be centred using a 2-point step.

Trend (long-term rise/fall), seasonality (pattern repeating at fixed intervals within a year), cycles (repeating over longer than a year), irregular (random) fluctuations, structural change (sudden lasting shift), outliers.

Deseasonalised value = actual value ÷ seasonal index; multiply to re-seasonalise. The indices average to 1 (their sum equals the number of seasons). SI = 1.30 means that season runs 30% above the seasonal average; SI = 0.85 means 15% below.

Two parts: a starting value and a rule linking consecutive terms, e.g. V0 = 5000, V(n+1) = 1.02×Vn − 80. It generates terms one step at a time, so it suits small n; use the explicit rule for large n.

Recurrence: u0 = a, u(n+1) = un + d (growth) or un − d (decay). Explicit rule: un = u0 + n×d (or − n×d). Plotted terms lie on a straight line. Models simple interest and flat rate depreciation.

Recurrence: u0 = a, u(n+1) = R×un. Explicit rule: un = Rⁿ × u0. If R > 1 the terms grow (compound interest); if 0 < R < 1 they decay (reducing balance depreciation).

Interest is calculated on the principal only, so the same amount is added each period: D = (r/100) × V0. Recurrence: V(n+1) = Vn + D; rule: Vn = V0 + n×D. An example of linear growth.

Value falls by the same dollar amount each year: D = (r/100) × V0, where r is the flat rate per annum. Recurrence: V(n+1) = Vn − D; rule: Vn = V0 − n×D. Linear decay.