Please check the examination details below before entering your
candidate information
Candidate surnameOther names
Centre Candidate
Number Number
Pearson Edexcel Level
3 GCE
Monday 26 June 2023
Afternoon (Time: 1 hour 30
Minutes) reference
Paper
9FM0/4
Further B
Mathematics
Advanced
PAPER 4B: Further
Statistics
You must have: 2 Total
Mathematical Formulae and Statistical Tables Marks
(Green), calculator
Candidates may use any calculator allowed by Pearson
regulations. Calculators must not have the facility for symbolic
algebra manipulation, differentiation and integration, or have
retrievable mathematical formulae stored in them.
Instructions
• Use black ink or ball-
• If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
• Fill
point
in the boxes at the top of this page with
centrepen.
number and candidate
number.all questions and ensure that your answers to parts of questions
• Answer
• your name,
Answer thelabelled.
are clearly questions in themay
– there spaces
be more space than you need.
• You should show sufficient working to make your methods clear.
•
Answers
provided without working may not gain full credit.
Values from statistical tables should be quoted in full. If a calculator is
used instead of tables the value should be given to an equivalent
• degree of accuracy.
Inexact answers should be given to three significant figures unless otherwise stated.
Informat
• A booklet ‘Mathematical Formulae and Statistical
ion
• There are 8 questions in this question paper. The total mark for
• this
The paper
marks is
for75. – use
each
Tables’ is provided.
this as a
question guide
are as to how much time to
shown
spend on each question.
Advice
•
in brackets
Read each question carefully before you start to answer it.
• Try to answer every Turn over
• Check your answers if you have time at the end.
question.
,1. Baako is investigating the times taken by children to run a 100 m race, x seconds, and
a 500 m race, y seconds. For a sample of 20 children, Baako obtains the time taken by
each child to run each race.
AREA
DO NOT WRITE IN THIS
Here are Baako’s summary statistics.
Sxx = 314.55 Syy = 9026 Sxy = 1610
x 19.65 y 108
(a) Calculate the product moment correlation coefficient between the times taken to run
the 100 m race and the times taken to run the 500 m race.
(2)
(b) Show that the equation of the regression line of y on x can be written as
y = 5.12x + 7.42
where the gradient and y intercept are given to 3 significant figures.
(3)
The child who completed the 100 m race in 20 seconds took 104 seconds to complete
the 500 m race.
AREA
DO NOT WRITE IN THIS
(c) Find the residual for this child.
(1)
The table below shows the signs of the residuals for the 20 children in order of finishing
time for the 100 m race.
Sign of residual + + + + – – + – – – – – – – – + + + + +
(d) Explain what the signs of the residuals show about the model’s predictions of the
500 m race times for the children who are fastest and slowest over the 100 m race.
(1)
AREA
DO NOT WRITE IN THIS
2
, Question 1 continued
DO NOT WRITE IN THIS
AREA
DO NOT WRITE IN THIS
AREA
DO NOT WRITE IN THIS
AREA
(Total for Question 1 is 7 marks)
3
Turn
over
candidate information
Candidate surnameOther names
Centre Candidate
Number Number
Pearson Edexcel Level
3 GCE
Monday 26 June 2023
Afternoon (Time: 1 hour 30
Minutes) reference
Paper
9FM0/4
Further B
Mathematics
Advanced
PAPER 4B: Further
Statistics
You must have: 2 Total
Mathematical Formulae and Statistical Tables Marks
(Green), calculator
Candidates may use any calculator allowed by Pearson
regulations. Calculators must not have the facility for symbolic
algebra manipulation, differentiation and integration, or have
retrievable mathematical formulae stored in them.
Instructions
• Use black ink or ball-
• If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
• Fill
point
in the boxes at the top of this page with
centrepen.
number and candidate
number.all questions and ensure that your answers to parts of questions
• Answer
• your name,
Answer thelabelled.
are clearly questions in themay
– there spaces
be more space than you need.
• You should show sufficient working to make your methods clear.
•
Answers
provided without working may not gain full credit.
Values from statistical tables should be quoted in full. If a calculator is
used instead of tables the value should be given to an equivalent
• degree of accuracy.
Inexact answers should be given to three significant figures unless otherwise stated.
Informat
• A booklet ‘Mathematical Formulae and Statistical
ion
• There are 8 questions in this question paper. The total mark for
• this
The paper
marks is
for75. – use
each
Tables’ is provided.
this as a
question guide
are as to how much time to
shown
spend on each question.
Advice
•
in brackets
Read each question carefully before you start to answer it.
• Try to answer every Turn over
• Check your answers if you have time at the end.
question.
,1. Baako is investigating the times taken by children to run a 100 m race, x seconds, and
a 500 m race, y seconds. For a sample of 20 children, Baako obtains the time taken by
each child to run each race.
AREA
DO NOT WRITE IN THIS
Here are Baako’s summary statistics.
Sxx = 314.55 Syy = 9026 Sxy = 1610
x 19.65 y 108
(a) Calculate the product moment correlation coefficient between the times taken to run
the 100 m race and the times taken to run the 500 m race.
(2)
(b) Show that the equation of the regression line of y on x can be written as
y = 5.12x + 7.42
where the gradient and y intercept are given to 3 significant figures.
(3)
The child who completed the 100 m race in 20 seconds took 104 seconds to complete
the 500 m race.
AREA
DO NOT WRITE IN THIS
(c) Find the residual for this child.
(1)
The table below shows the signs of the residuals for the 20 children in order of finishing
time for the 100 m race.
Sign of residual + + + + – – + – – – – – – – – + + + + +
(d) Explain what the signs of the residuals show about the model’s predictions of the
500 m race times for the children who are fastest and slowest over the 100 m race.
(1)
AREA
DO NOT WRITE IN THIS
2
, Question 1 continued
DO NOT WRITE IN THIS
AREA
DO NOT WRITE IN THIS
AREA
DO NOT WRITE IN THIS
AREA
(Total for Question 1 is 7 marks)
3
Turn
over
