Measurement, Statistics and Probability in Context
Core concepts
This section covers practical measurement and everyday data. You need perimeter and area of rectangles, triangles, circles and composite shapes; volume of prisms and cylinders; surface area where relevant; and the ability to work with scale drawings and plans. In statistics, know how to read and construct tables, bar and line graphs, pie charts, histograms and scatterplots; calculate mean, median, mode and range; and interpret spread and outliers. In probability, use fractions, decimals and percentages to express likelihood, understand complementary events, and use simple two-way tables and tree diagrams for combined events.
Traps to watch
- Units. Convert to a common unit before calculating; give area in square units and volume in cubic units.
- Composite shapes. Decide whether to add or subtract the parts, and do not double-count shared edges.
- Circle formulas. Diameter is twice the radius; using the diameter in place of the radius is the most common error.
- Mean versus median. An outlier drags the mean but barely moves the median; questions often ask which is more representative.
- Pie chart angles. Each category's angle equals its fraction of the total multiplied by 360°.
- Independent events. Multiply probabilities only when events are independent; the complement rule gives P(not A) = 1 − P(A).
Worked example
A rectangular garden 8 m by 5 m has a circular pond of radius 1.5 m. Find the planted area, using π ≈ 3.14. Garden area = 8 × 5 = 40 m². Pond area = πr² = 3.14 × 2.25 = 7.065 m². Planted area = 40 − 7.065 ≈ 32.9 m². Rule of thumb: sketch the shape, label every measurement in the same unit, then decide add or subtract before substituting numbers. Check that the answer is smaller than the whole shape when a piece is removed.