OCR
GCSE
Further Mathematics A
Y532/01: Statistics
*1919957079*
AS Level
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 page 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 non-exact numerical answers correct to 3 significant figures unless a different
degree of accuracy is specified in the question.
• The acceleration due to gravity is denoted by g m s–2. When a numerical value is
needed use g = 9.8 unless a different value is specified in the question.
• 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 4 pages.
ADVICE
• Read each question carefully before you start your answer.
© OCR 2025 [M/508/5498] DC (PQ) 356310/3
OCR is an exempt Charity
Turn over
1 A six-sided dice may or may not be equally likely to land on any one of its faces. It
has two faces numbered 5 and the other four faces are numbered 1, 2, 3 and 4. The
dice is thrown 60 times, and the outcome on each throw is recorded. The results are
shown in the table.
Outcome 1 2 3 4 5
, 2
Frequency 7 13 11 15 14
It is required to carry out a test at the 5% significance level of whether the
probabilities of the outcomes 1, 2, 3, 4 and 5 are in the ratio 1 : 1 : 1 : 1 : 2.
(a) State suitable hypotheses for the test. [1]
(b) Carry out the test. [6]
2 On any day, flights of helicopters and aeroplanes pass within sight of a certain
building only during a daytime period of 12 hours, from 7.00 am to 7.00 pm.
The random variable H is the number of helicopters that pass within sight of the
building during a randomly chosen daytime period of 12 hours.
(a) State two assumptions needed for H to be well modelled by a Poisson
distribution. [2]
Assume now that H can be well modelled by the distribution Po(1.8).
(b) Find the probability that, during a randomly chosen daytime period of 12
hours, the number of helicopters that pass within sight of the building is 2, 3
or 4. [2]
(c) During a period of t hours (within the daytime period of 12 hours), the
probability that no helicopters pass within sight of the building is 0.95.
Use an algebraic method to determine the value of t.
(d) During a randomly chosen daytime period of t hours (where t is the value
found in part (c)) two helicopters pass within sight of the building.
Explain whether this casts doubt on the validity of the model. You do not need to
carry out
any calculations.
Throughout the daytime period of 12 hours on any day, aeroplanes pass within sight
of the building at a fixed constant rate of 1 aeroplane every 4 minutes.
(e) Explain whether the number of aeroplanes that pass within sight of the
building on any day is
likely to be well modelled by a Poisson distribution.
(f) Find the expected value of the total number of helicopters and aeroplanes
that pass within
sight of the building on a randomly chosen day.
© OCR 2025 Y532/01 Jun25
, 3
3 (a) It is required to test whether there is a relationship between two numerical
variables.
State why in certain circumstances it would be better to use a test based on
Spearman’s rank
correlation coefficient rather than a test based on the product-moment correlation
coefficient.
(b) A publisher wants to test whether there is any association between the
ratings given by two readers, A and B, to books. The publisher selects 7 books
at random and gives a copy of each book to each reader. Each reader gives a
rating out of 20, where 20 is high and 0 is low, to each of the 7 books. The
ratings are shown in the table.
Book P Q R S T U V
Reader A 3 7 8 12 13 18 19
Reader B 17 15 16 14 4 5 13
(i)
In the Printed Answer Booklet, complete the table giving the ranks
of the ratings given
by Reader A and Reader B.
(ii) Use Spearman’s rank correlation coefficient to test at the 5%
significance level whether
there is any association between the readers’ ratings of books.
4 In a science experiment, the values of a variable W are selected by the scientist. The
experiment involves measuring the corresponding values of the variable V. The
results are summarised as follows. n = 10 /v = 176 2. /w = 87 5. /v2 = 4077 64.
/w2 = 951 25. /vw = 1963 4.
(a) Calculate the value of the product-moment correlation coefficient. [2]
(b) By identifying the controlled variable in the experiment, calculate the
equation of the
appropriate least squares regression line.
It is required to obtain an estimate of the value of the response variable when the
value of the controlled variable is 10.0.
(c) (i) Find the value of the required estimate. [1]
(ii) Use the appropriate mean and standard deviation to determine whether
10.0 is likely to
be within the range of the data for the controlled variable.
© OCR 2025 Y532/01 Jun25
GCSE
Further Mathematics A
Y532/01: Statistics
*1919957079*
AS Level
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 page 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 non-exact numerical answers correct to 3 significant figures unless a different
degree of accuracy is specified in the question.
• The acceleration due to gravity is denoted by g m s–2. When a numerical value is
needed use g = 9.8 unless a different value is specified in the question.
• 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 4 pages.
ADVICE
• Read each question carefully before you start your answer.
© OCR 2025 [M/508/5498] DC (PQ) 356310/3
OCR is an exempt Charity
Turn over
1 A six-sided dice may or may not be equally likely to land on any one of its faces. It
has two faces numbered 5 and the other four faces are numbered 1, 2, 3 and 4. The
dice is thrown 60 times, and the outcome on each throw is recorded. The results are
shown in the table.
Outcome 1 2 3 4 5
, 2
Frequency 7 13 11 15 14
It is required to carry out a test at the 5% significance level of whether the
probabilities of the outcomes 1, 2, 3, 4 and 5 are in the ratio 1 : 1 : 1 : 1 : 2.
(a) State suitable hypotheses for the test. [1]
(b) Carry out the test. [6]
2 On any day, flights of helicopters and aeroplanes pass within sight of a certain
building only during a daytime period of 12 hours, from 7.00 am to 7.00 pm.
The random variable H is the number of helicopters that pass within sight of the
building during a randomly chosen daytime period of 12 hours.
(a) State two assumptions needed for H to be well modelled by a Poisson
distribution. [2]
Assume now that H can be well modelled by the distribution Po(1.8).
(b) Find the probability that, during a randomly chosen daytime period of 12
hours, the number of helicopters that pass within sight of the building is 2, 3
or 4. [2]
(c) During a period of t hours (within the daytime period of 12 hours), the
probability that no helicopters pass within sight of the building is 0.95.
Use an algebraic method to determine the value of t.
(d) During a randomly chosen daytime period of t hours (where t is the value
found in part (c)) two helicopters pass within sight of the building.
Explain whether this casts doubt on the validity of the model. You do not need to
carry out
any calculations.
Throughout the daytime period of 12 hours on any day, aeroplanes pass within sight
of the building at a fixed constant rate of 1 aeroplane every 4 minutes.
(e) Explain whether the number of aeroplanes that pass within sight of the
building on any day is
likely to be well modelled by a Poisson distribution.
(f) Find the expected value of the total number of helicopters and aeroplanes
that pass within
sight of the building on a randomly chosen day.
© OCR 2025 Y532/01 Jun25
, 3
3 (a) It is required to test whether there is a relationship between two numerical
variables.
State why in certain circumstances it would be better to use a test based on
Spearman’s rank
correlation coefficient rather than a test based on the product-moment correlation
coefficient.
(b) A publisher wants to test whether there is any association between the
ratings given by two readers, A and B, to books. The publisher selects 7 books
at random and gives a copy of each book to each reader. Each reader gives a
rating out of 20, where 20 is high and 0 is low, to each of the 7 books. The
ratings are shown in the table.
Book P Q R S T U V
Reader A 3 7 8 12 13 18 19
Reader B 17 15 16 14 4 5 13
(i)
In the Printed Answer Booklet, complete the table giving the ranks
of the ratings given
by Reader A and Reader B.
(ii) Use Spearman’s rank correlation coefficient to test at the 5%
significance level whether
there is any association between the readers’ ratings of books.
4 In a science experiment, the values of a variable W are selected by the scientist. The
experiment involves measuring the corresponding values of the variable V. The
results are summarised as follows. n = 10 /v = 176 2. /w = 87 5. /v2 = 4077 64.
/w2 = 951 25. /vw = 1963 4.
(a) Calculate the value of the product-moment correlation coefficient. [2]
(b) By identifying the controlled variable in the experiment, calculate the
equation of the
appropriate least squares regression line.
It is required to obtain an estimate of the value of the response variable when the
value of the controlled variable is 10.0.
(c) (i) Find the value of the required estimate. [1]
(ii) Use the appropriate mean and standard deviation to determine whether
10.0 is likely to
be within the range of the data for the controlled variable.
© OCR 2025 Y532/01 Jun25
