Oxford Cambridge and RSA
Friday 7 June 2024 – Afternoon
A Level Further Mathematics A
Y542/01 Statistics
Time allowed: 1 hour 30 minutes
You must have:
• the Printed Answer Booklet
• the Formulae Booklet for A Level Further
QP
Mathematics A
• a scientific or graphical calculator
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 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 75.
• 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 is an exempt Charity
Turn over
,
, 2
1 A discrete random variable X has the following distribution, where a, b and c are constants.
x 0 1 2 3
P(X = x) a b c 0.1
It is given that E(X ) = 1.25 and Var (X ) = 0.8875.
(a) Determine the values of a, b and c. [5]
(b) The random variable Y is defined by Y = 7 - 2 X .
Write down the value of Var (Y ). [1]
(c) Twenty independent observations of X are obtained. The number of those observations
for which X = 3 is denoted by T.
Find the value of Var (T ). [2]
2 A newspaper article claimed that “taller dog owners have taller dogs as pets”. Alex investigated
this claim and obtained data from a random sample of 16 fellow students who owned exactly
one dog. The results are summarised as follows, where the height of the student, in cm, is
denoted by h and the height, in cm, of their dog is denoted by d.
n = 16 / h = 2880 / d = 660 / h 2 = 519276 / d 2 = 30000 /hd = 119425
(a) Calculate the value of Pearson’s product moment correlation coefficient for the data. [2]
(b) State what your answer tells you about a scatter diagram illustrating the data. [1]
(c) Use the data to test, at the 5% significance level, the claim of the newspaper article. [5]
(d) Explain whether the answer to part (a) would be likely to be different if the dogs’ weights
had been used instead of their heights. [1]
© OCR 2024 Y542/01 Jun24
Friday 7 June 2024 – Afternoon
A Level Further Mathematics A
Y542/01 Statistics
Time allowed: 1 hour 30 minutes
You must have:
• the Printed Answer Booklet
• the Formulae Booklet for A Level Further
QP
Mathematics A
• a scientific or graphical calculator
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 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 75.
• 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 is an exempt Charity
Turn over
,
, 2
1 A discrete random variable X has the following distribution, where a, b and c are constants.
x 0 1 2 3
P(X = x) a b c 0.1
It is given that E(X ) = 1.25 and Var (X ) = 0.8875.
(a) Determine the values of a, b and c. [5]
(b) The random variable Y is defined by Y = 7 - 2 X .
Write down the value of Var (Y ). [1]
(c) Twenty independent observations of X are obtained. The number of those observations
for which X = 3 is denoted by T.
Find the value of Var (T ). [2]
2 A newspaper article claimed that “taller dog owners have taller dogs as pets”. Alex investigated
this claim and obtained data from a random sample of 16 fellow students who owned exactly
one dog. The results are summarised as follows, where the height of the student, in cm, is
denoted by h and the height, in cm, of their dog is denoted by d.
n = 16 / h = 2880 / d = 660 / h 2 = 519276 / d 2 = 30000 /hd = 119425
(a) Calculate the value of Pearson’s product moment correlation coefficient for the data. [2]
(b) State what your answer tells you about a scatter diagram illustrating the data. [1]
(c) Use the data to test, at the 5% significance level, the claim of the newspaper article. [5]
(d) Explain whether the answer to part (a) would be likely to be different if the dogs’ weights
had been used instead of their heights. [1]
© OCR 2024 Y542/01 Jun24
