The speeds, in kmh⁻¹, of 90 cars as they passed a certain marker on a road were recorded, correct to the nearest kmh⁻¹. The results are summarised in the following table. Speed (kmh⁻¹) 10–29 30–39 40–49 50–59 60–89 Frequency 10 24 30 14 12

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.

1. [M1] At least 3 frequency densities calculated (frequency ÷ class width) e.g. (10/20, 10/19, 10/19.5) may be read from graph using their scale, 3SF or exact
2. [A1] All heights correct on graph.
3. [B1] Bar ends of 9.5, 29.5, 39.5, 59.5, 89.5
4. [B1] Axes labelled: Frequency density (fd) and speed/km h⁻¹ (or appropriate title). Linear scales 9.5 ≤ horizontal axis < 89.5, 0 < vertical axis < 3, 5 bars with no gaps
5. [M1] Uses at least 4 midpoint attempts (e.g. 19.5 ± 0.5). Allow unsimplified expression. (19.5×10+34.5 × 24 + 44.5×30+54.5×14+74.5×12) / 90
6. [A1] Final answer not an improper fraction 44 11/18 or 44.6 (km h⁻¹) NFWW