The times, to the nearest minute, of 150 athletes taking part in a charity run are recorded. The results are summarised in the table. Time in minutes | 101–120 | 121–130 | 131–135 | 136–145 | 146–160 Frequency | 18 | 48 | 34 | 32 | 18

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2023). The mark or mark type is shown in brackets.

1. [M1] At least 4 frequency densities calculated by f/cw e.g. 18/20 (condone f/cw ±0.5 if unsimplified). Accept unsimplified, may be read from graph using their scale, no lower than 1cm = 1 fd.
2. [A1] All bar heights correct on graph (no FT), using their suitable linear scale with at least 3 values indicated, no lower than 1cm = 1 fd.
3. [B1] Bar ends at 120.5, 130.5, 135.5, 145.5, 160.5. 5 bars drawn with a horizontal linear scale, no lower than 1 cm = 10 min, with at least 3 values indicated. 100 ≤ horizontal scale ≤ 160.
4. [B1] Axes labelled frequency density (fd), time (t) and minutes (min, m) oe, or an appropriate title. (Axes may be reversed).
5. [B1] At least 4 correct mid-points seen, may be by data table or used in formula.
6. [M1] Correct formula for mean using midpoints ±0.5, condone 1 midpoint error within class.
7. [A1] Accept 132, 131 9/10, or 1319/10. Must be identified.
8. [M1] Appropriate variance formula with their 5 midpoints within class (not upper bound, lower bound, class width, frequency density, frequency or cumulative frequency). Condone 1 error. If correct midpoints seen, accept (3200+41400+194400+157300+153600)/150 - {131.9² or 17397.61}.
9. [A1] 11.7277448... to at least 3SF. Accept 11.6 ≤ σ < 11.95 www. If MO awarded, SC B1 11.6 ≤ σ < 11.95 www.