Each year the total number of hours, x, of sunshine in Kintoo is recorded during the month of June. The results for the last 60 years are summarised in the table. X 30 < x < 60 60 < x < 90 90 < x < 110 110 < x < 140 140 < x < 180 180 ≤ x ≤ 240 Number of years 4 8 14 25 7 2

Mark scheme

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

1. [B1] All cumulative frequencies stated. May be under data table, condone omission of 4. May be read accurately from graph, must include 4.
2. [M1] At least 5 points plotted at class upper end points, daylight rule tolerance. Linear cf scale 0 < cf < 60, linear time scale 30 < time < 240 with at least 3 values identified on each axis.
3. [A1] All points plotted correctly. Curve drawn (within tolerance), no ruled segments, and joined to (30,0). Axes labelled 'cumulative frequency' and 'hours [of sunshine]' (OE including appropriate title).
4. [M1] [60 × 0.7 = ] 42. 42 may be implied by clear use on graph.
5. [A1 FT] Must be clear evidence on graph of use of 42, e.g. an appropriate mark on either axis, appropriate mark on curve. FT from increasing cf graph only read at 42 only.
6. [B1] Midpoints: 45, 75, 100, 125, 160, 210. At least 5 correct mid-points seen, check by data table or used in formula.
7. [M1] Correct mean formula using their 6 midpoints (must be within class, not upper bound, lower bound), condone 1 data error. If correct midpoints seen accept (180+600+1400+3125+1120+420)/60.
8. [A1] [Mean =] (4×45+8×75+14×100+25×125+7×160+2×210)/60 = 6845/60 = 114, 114 1/12. Accept 114.1, 114.08[3...]. If A1 not awarded, SC B1 for 114, 114 1/12, 114.1 or 114.08[3...].