On a certain day, the heights of 150 sunflower plants grown by children at a local school are measured, correct to the nearest cm. These heights are summarised in the following table. Height (cm): 10-19, 20-29, 30-39, 40-44, 45-49, 50-54, 55-59 Frequency: 10, 18, 32, 42, 28, 14, 6

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2024). The mark or mark type is shown in brackets.

1. [B1] Cf values 28, 60, 102, 130, 144, 150 seen, Condone omission of 10. May be implied by accurate plotting (scale no less than 1cm = 10). May be by data table.
2. [B1] Linearly scaled axes correctly labelled cumulative frequency (cf) (from 0 to 150) and height (h) and centimetres (cm) (from 9.5 to 59.5) with at least 3 values identified on each. Axes can be the other way round.
3. [M1] At least 4 points plotted at upper boundary ± 0.5, (e.g. allow (19, 19.5 or 20, 10) etc.) on correctly scaled axes. (9.5,0), (19.5,10), (29.5, 28), (39.5, 60), (44.5,102), (49.5, 130), (54.5, 144), (59.5,150).
4. [A1] All points plotted correctly, curve drawn (within tolerance), joined to (9.5, 0) and not going beyond above 150 vertically. A0 if straight line segments used.
5. [M1] Use of graph must be seen.
6. [A1 FT] Must be an increasing cf graph. Expect an answer in range 35 < h < 37 for a correct graph.
7. [B1] At least 6 correct midpoints seen, may be unsimplified, may be in calculation, may be by data table.
8. [M1] Correct unsimplified mean formula with their midpoints (not ub, lb, upper limits, lower limits, cw, fd, f or cf and must be within class). If midpoints correct, accept partially evaluated.
9. [A1] Accept answers wrt 38.9 WWW If M1 withheld, SC B1 for 5840/150, 584/15, 38.9.
10. [M1] Correct unsimplified variance formula with their midpoint (not ub, lb, upper limits, lower limits, cw, fd, f or cf and must be within class). If midpoints correct, accept partially evaluated
11. [A1] AWRT 10.6 WWW. If second M1 withheld, SC B1 for 10.6 WWW.