The weights, xkg, of 120 students in a sports college are recorded. The results are summarised in the following table. Weight (xkg) | x ≤ 40 | x ≤ 60 | x ≤ 65 | x ≤ 70 | x ≤ 85 | x ≤ 100 Cumulative frequency | 0 | 14 | 38 | 60 | 106 | 120

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 3 points plotted accurately at class upper end points (40,0) (60,14) (65,38) (70,60) (85,106) (100,120). Linear cumulative frequency scale 0 < cf < 120 and linear weight scale 40 < weight(kg) ≤ 100 with at least 3 values identified on each axis. Condone scale reversed.
2. [A1] All points plotted correctly, curve drawn (within tolerance) and joined to (40,0). Axes labelled cumulative frequency (cf), weight (w) and kg (kilograms) – or a suitable title.
3. [M1] [120 × 0.65 = ] 78 seen May be implied by use on graph.
4. [A1] 75 < hours < 79. Indication of use of graph required.
5. [B1] At least 5 correct frequencies seen (condone omission of 0).
6. [B1] At least 5 correct midpoints seen (condone omission of 20).
7. [M1] Correct formula for mean using their midpoints and their frequencies, implied by 8545/120 if correct midpoints & frequencies seen. May be gained in variance calculation. If midpoints not clearly identified, condone midpoints ±0.5.
8. [A1] Accept 1709/24 or 71 5/24 or 71.208333 to at least 3SF. If M0 scored, SC B1 for 1709/24 or 71 5/24 or 71.208333 to at least 3SF www.
9. [M1] Correct formula for variance using their midpoints, their frequencies and their mean. Implied by 625062.5/120 - (8545/120)² if correct midpoints & frequencies seen.
10. [A1] 11.757016 to at least 3SF.