Oxford Cambridge and RSA
May 2026 – Afternoon AS
Level Further Mathematics B (MEI) Y412/01
Statistics a
Time allowed: 1 hour 15 minutes
You must have:
• the Printed Answer Booklet
• the Formulae Booklet for Further Mathematics B
(MEI)
• a scientific or graphical calculator
QP
INSTRUCTIONS
• Use black ink. You can use an HB pencil, but only for graphs and diagrams.
• Write your answer to each question in the space provided in the Printed Answer Booklet. If
you need extra space use the lined pages at the end of the Printed Answer Booklet. The
question numbers must be clearly shown.
• Fill in the boxes on the front of the Printed Answer Booklet.
• Answer all the questions.
• Where appropriate, your answer should be supported with working. Marks might be given
for using a correct method, even if your answer is wrong.
• Give your final answers to a degree of accuracy that is appropriate to the context.
• Do not send this Question Paper for marking. Keep it in the centre or recycle it.
INFORMATION
• The total mark for this paper is 60.
• The marks for each question are shown in brackets [ ].
• This document has 8 pages.
ADVICE
• Read each question carefully before you start your answer
OCR AS Level Further Mathematics B (MEI) Statistics (Y412/01) Question
Paper And Mark Scheme
, 2
1 A student is investigating what level of exercise is given to dogs in the UK by their owners.
(a) When trying to collect suitable information, give two reasons why it might be advantageous
to use a sample of dog owners, rather than a census of dog owners. [2]
(b) Explain why it is preferable that the size of the sample is large. [1]
2 The probability distribution of a discrete random variable X is given in the table.
x 0 1 2 3
1 1 1
P(X = x) a
6 3 10
(a) Find the value of a. [1]
The probability function of another discrete random variable, Y, is defined below.
y
P(Y = y) =
595 for y = 1, 2, ..., n,
where n is a positive integer.
(b) Determine the value of n. [3]
(c) Find P(Y 1 n). [1]
(d) Given that X and Y are independent, determine P(X + Y G 2). [2]
3 The discrete random variable Q has the distribution Geo(0.3).
(a) Find P(Q = 2). [1]
(b) Determine P(Q G 5). [2]
The discrete random variable R has a uniform distribution on {4, 5, ..., 8}.
The discrete random variable S has the distribution B(10, 0.1).
Q, R and S are mutually independent of each other.
(c) Find P(Q + R + S = 5) [3]
The discrete random variable T is defined by T = R - Q + 2S
(d) Determine the value of E(T). [4]
© OCR 2025 Y412/01 Jun25
, 3
4 A scientist measures the length, x cm, and mass, y kg, of a random sample of 34 adult
female badgers. A scatter diagram for the data is shown in the diagram.
y
13
11
Badger mass (kg)
9
7
0 x
0 64 66 68 70 72 74 76 78 80
Badger length (cm)
(a) Give two reasons why it would be appropriate for a hypothesis test based on the
product‑moment correlation coefficient to be carried out in this situation. [2]
The scientist analyses the collected data and produces the following summary statistics.
n = 34 /x = 2409.4 / y = 350.87 /x2 = 171140.28 /y2 = 3681.851 /xy = 24981.486
(b) Find and use the equation of a suitable regression line to determine an estimate of the
length of an adult female badger of mass 10 kg. [4]
© OCR 2025 Y412/01 Jun25 Turn over
, 4
5 Two judges, Judge A and Judge B, independently rank 8 entries in a jam‑making competition,
awarding each jam a rank from 1 (best) to 8 (worst). There are no tied ranks. The ranks are
shown in the table below but unfortunately two of the rankings awarded by Judge B have been
lost.
Jam 1 Jam 2 Jam 3 Jam 4 Jam 5 Jam 6 Jam 7 Jam 8
Judge A 4 8 7 1 5 6 3 2
Judge B 4 5 2 6 1 3
(a) Explain which jam is likely to be the best. [1]
Before Judge B’s ranks were lost, Spearman’s rank correlation coefficient was calculated for all
6
the data and found to be7 .
(b) Determine the missing ranks that Judge B gave, specifying which rank was given to which
jam. [3]
The two judges want to assess whether there is positive association between their rankings of jam.
(c) Carry out a hypothesis test to make the assessment using a significance level of 1%. [5]
© OCR 2025 Y412/01 Jun25
May 2026 – Afternoon AS
Level Further Mathematics B (MEI) Y412/01
Statistics a
Time allowed: 1 hour 15 minutes
You must have:
• the Printed Answer Booklet
• the Formulae Booklet for Further Mathematics B
(MEI)
• a scientific or graphical calculator
QP
INSTRUCTIONS
• Use black ink. You can use an HB pencil, but only for graphs and diagrams.
• Write your answer to each question in the space provided in the Printed Answer Booklet. If
you need extra space use the lined pages at the end of the Printed Answer Booklet. The
question numbers must be clearly shown.
• Fill in the boxes on the front of the Printed Answer Booklet.
• Answer all the questions.
• Where appropriate, your answer should be supported with working. Marks might be given
for using a correct method, even if your answer is wrong.
• Give your final answers to a degree of accuracy that is appropriate to the context.
• Do not send this Question Paper for marking. Keep it in the centre or recycle it.
INFORMATION
• The total mark for this paper is 60.
• The marks for each question are shown in brackets [ ].
• This document has 8 pages.
ADVICE
• Read each question carefully before you start your answer
OCR AS Level Further Mathematics B (MEI) Statistics (Y412/01) Question
Paper And Mark Scheme
, 2
1 A student is investigating what level of exercise is given to dogs in the UK by their owners.
(a) When trying to collect suitable information, give two reasons why it might be advantageous
to use a sample of dog owners, rather than a census of dog owners. [2]
(b) Explain why it is preferable that the size of the sample is large. [1]
2 The probability distribution of a discrete random variable X is given in the table.
x 0 1 2 3
1 1 1
P(X = x) a
6 3 10
(a) Find the value of a. [1]
The probability function of another discrete random variable, Y, is defined below.
y
P(Y = y) =
595 for y = 1, 2, ..., n,
where n is a positive integer.
(b) Determine the value of n. [3]
(c) Find P(Y 1 n). [1]
(d) Given that X and Y are independent, determine P(X + Y G 2). [2]
3 The discrete random variable Q has the distribution Geo(0.3).
(a) Find P(Q = 2). [1]
(b) Determine P(Q G 5). [2]
The discrete random variable R has a uniform distribution on {4, 5, ..., 8}.
The discrete random variable S has the distribution B(10, 0.1).
Q, R and S are mutually independent of each other.
(c) Find P(Q + R + S = 5) [3]
The discrete random variable T is defined by T = R - Q + 2S
(d) Determine the value of E(T). [4]
© OCR 2025 Y412/01 Jun25
, 3
4 A scientist measures the length, x cm, and mass, y kg, of a random sample of 34 adult
female badgers. A scatter diagram for the data is shown in the diagram.
y
13
11
Badger mass (kg)
9
7
0 x
0 64 66 68 70 72 74 76 78 80
Badger length (cm)
(a) Give two reasons why it would be appropriate for a hypothesis test based on the
product‑moment correlation coefficient to be carried out in this situation. [2]
The scientist analyses the collected data and produces the following summary statistics.
n = 34 /x = 2409.4 / y = 350.87 /x2 = 171140.28 /y2 = 3681.851 /xy = 24981.486
(b) Find and use the equation of a suitable regression line to determine an estimate of the
length of an adult female badger of mass 10 kg. [4]
© OCR 2025 Y412/01 Jun25 Turn over
, 4
5 Two judges, Judge A and Judge B, independently rank 8 entries in a jam‑making competition,
awarding each jam a rank from 1 (best) to 8 (worst). There are no tied ranks. The ranks are
shown in the table below but unfortunately two of the rankings awarded by Judge B have been
lost.
Jam 1 Jam 2 Jam 3 Jam 4 Jam 5 Jam 6 Jam 7 Jam 8
Judge A 4 8 7 1 5 6 3 2
Judge B 4 5 2 6 1 3
(a) Explain which jam is likely to be the best. [1]
Before Judge B’s ranks were lost, Spearman’s rank correlation coefficient was calculated for all
6
the data and found to be7 .
(b) Determine the missing ranks that Judge B gave, specifying which rank was given to which
jam. [3]
The two judges want to assess whether there is positive association between their rankings of jam.
(c) Carry out a hypothesis test to make the assessment using a significance level of 1%. [5]
© OCR 2025 Y412/01 Jun25
