June 2025 Paper 2 Q8

OCR MEICurrent spec4 marksData Processing

8 At the end of the summer term all 120 Year 8 pupils at Oakmount College sit the same mathematics examination.

The marks obtained by the pupils in the 2024 examination are summarised in the table.

Mark	11–20	21–30	31–40	41–50	51–60	61–70	71–80	81–90	91–100
Frequency	8	12	24	17	23	16	10	7	3

Software is used to produce the cumulative frequency curve shown below.

Cumulative frequency curve of examination mark, from (10, 0) through (20, 8), (30, 20), (40, 44), (50, 61), (60, 84), (70, 100), (80, 110), (90, 117) to (100, 120)

(a) It is proposed that the 30 pupils with the best marks in the examination are placed in the top set in Year 9.

Use the copy of the cumulative frequency curve in the Printed Answer Booklet to determine an estimate of the lowest mark needed for a pupil to be placed in the top set. [2]

(b) The person who will teach the top set states that pupils will not manage in this class unless they obtain at least 75 marks in the examination.

Use the copy of the cumulative frequency curve in the Printed Answer Booklet to determine an estimate of how many pupils will be in the top set if the lowest mark is set at 75. [2]

Mark scheme (a)

Scheme	Marks	AO
eg horizontal line at cf = 90 or 91; eg curve marked at cf = 90 or 91 and mark stated eg vertical axis marked at 90 or 91 and mark stated eg horizontal axis marked between 60 and 65 and mark stated	M1	1.1
62, 63 or 64	A1	1.1
	[2]

Notes

M1: allow if seen on diagram for part (b)

A1: if M0 allow B1 for 62, 63 or 64

Mark scheme (b)

Scheme	Marks	AO
eg vertical line from mark = 75 eg curve marked at \(x\) = 75 and cf stated eg horizontal axis marked at 75 and cf stated eg vertical axis marked at 104 – 106 and cf stated	M1	1.1
14, 15 or 16	A1	1.1
	[2]

Notes

M1: allow if seen on diagram for part (a)

A1: if M0 allow B1 for 14, 15 or 16