The times of 240 competitors taking part in an event are recorded correct to the nearest minute. The results are summarised in the table. Time (minutes) | 1-10 | 11-20 | 21-25 | 26-30 | 31-50 Frequency | 12 | 38 | 68 | 76 | 46

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2025). The mark or mark type is shown in brackets.

1. [M1] At least 4 correct frequency densities (F/CW, e.g. 12/10, 38/10, 68/5, 76/5, 46/20). Accept un-simplified. May be read from graph if scale sufficiently accurate.
2. [A1] All heights correct on graph. Daylight rule applied full width of bar. Minimum scale: FD axis uses at least ½ the grid.
3. [B1] Bar ends at 0.5, 10.5, 20.5, 25.5, 30.5, 50.5, with a linear scale, 0.5 to 50.5, and at least 3 values indicated ‘linearly’. Daylight rule applied 0 cm < FD < 1 cm vertically.
4. [B1] Axes labelled frequency density (OE e.g. fd) and time, minutes (OE e.g. t, min). FD scale starts at 0 with a linear scale and at least 3 values indicated 'linearly'. (condone 0.5 on time scale and no value on FD scale). Minimum: time scale use at least ½ the grid. Axes can be reversed.
5. [M1] At least 4 correct midpoints. Midpoints: 5.5, 15.5, 23, 28, 40.5. May be seen by data table, accept un-simplified.
6. [M1] Correct mean formula using their 5 midpoints (must be within class, not upper bound, not lower bound), condone 1 error.
7. [A1] Accept 207/8 or 25 7/8 or 25.88 or 25.9 WWW. If 1 or more M not scored, SCB1 for 207/8 or 25.875 WWW.