Free VCE Year 11 General Mathematics Flashcard Review

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Difference between nominal and ordinal data?

Both are categorical; ordinal categories have a natural order (e.g. S, M, L), nominal categories do not (e.g. eye colour).

Is 'number of pets' discrete or continuous?

Discrete: it can only take whole-number counts.

Why is temperature in °C an interval (not ratio) scale?

Zero °C is not a true absence of heat, so differences make sense but ratios do not.

Best display for categorical data?

A bar chart (or percentage segmented bar chart for comparing groups).

Position of the median in n ordered values?

(n + 1) ÷ 2

Formula for sample standard deviation

s = √(Σ(x − x̄)² ÷ (n − 1))

What does SCOR stand for when describing a distribution?

Shape, Centre, Outliers, Range (spread).

Outlier fences

Lower: Q1 − 1.5 × IQR; upper: Q3 + 1.5 × IQR.

Which summary statistics are resistant to outliers?

The median and the IQR.

In a positively skewed distribution, how do mean and median compare?

The mean is usually greater than the median.

68–95–99.7% rule

In a bell-shaped distribution about 68%, 95% and 99.7% of values lie within 1, 2 and 3 standard deviations of the mean.

When does one group's median give strong evidence of a difference?

When it lies outside the box (Q1 to Q3) of the other group's boxplot.

What two parts does a recurrence relation need?

An initial value (e.g. u₀ = 5) and a rule linking consecutive terms (e.g. uₙ₊₁ = uₙ + 3).

Explicit rule for an arithmetic sequence

uₙ = a + nd, where a = u₀ and d is the common difference.

How should the graph of a sequence be drawn?

As isolated points with n on the horizontal axis; the points are not joined.

Explicit rule for a geometric sequence

uₙ = a × Rⁿ, where a = u₀ and R is the common ratio.

Multiplier R for a 7% increase and for a 7% decrease

Increase: R = 1.07. Decrease: R = 0.93.

Simple interest per period on principal P at r%

D = (r ÷ 100) × P, added every period.

Flat-rate vs reducing balance depreciation

Flat-rate: fixed % of purchase price (linear). Reducing balance: fixed % of current value (geometric).

Unit-cost depreciation per year

Cost per unit of use × number of units used in the year.