Edexcel Maths A Level Paper 31
Statistics QP
,
, Please check the examination details below before entering your candidate information
Candidate surname Other names
Centre Number Candidate Number
Pearson Edexcel Level 3 GCE
Monday 18 October 2021 – Afternoon ▲ ▲
Mathematics
Advanced
Paper
reference 9MA0/31
PAPER 31: Statistics
You must have:
Candidates may use any calculator allowed by Pearson regulations.Total Marks
Mathematical
Calculators Formulae
must notand Statistical
have Tables
the facility for(Green),
symboliccalculator
algebra manipulation,
differentiation and integration, or have retrievable mathematical formulae
stored in them.
Instructions
•• IfUsepencil
black ink or ball‑point pen.
• centre number
is used for diagrams/sketches/graphs it must be dark (HB or B).
Fill in the boxes at the top of this page with your name,
• Answer
and candidate number.
all questions and ensure that your answers to parts of questions are
• Answer
clearly labelled.
the questions in the spaces provided
• You
– there may be more space than you need.
should show sufficient working to make your methods clear.
• Values
Answers without working may not gain full credit.
from statistical tables should be quoted in full. If a calculator is used instead of
• Inexact answers should be given to three significant figures unless otherwise stated.
tables the value should be given to an equivalent degree of accuracy.
Information
•• The
A booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
total mark for this part of the examination is 50. There are 6 questions.
• –Theusemarks
this asfor eachas
a guide question are shown
to how much in spend
time to brackets
on each question.
• Read each question carefully before you start to answer it.
Advice
•• Check
Try to answer every question.
your answers if you have time at the end. Turn over
P68828A Downloaded by: brianryan1 |
©2021 Pearson Education Ltd.
Distribution of this document is illegal
A:1/1/1/1/1/
,1. (a) State one disadvantage of using quota sampling compared with simple random
sampling.
(1)
In a university 8% of students are members of the university dance club.
A random sample of 36 students is taken from the university.
The random variable X represents the number of these students who are members of the dance club.
(b) Using a suitable model for X, find
(i) P(X = 4)
(ii) P(X 7)
(3)
Only 40% of the university dance club members can dance the tango.
(c) Find the probability that a student is a member of the university dance club and can
dance the tango.
(1)
A random sample of 50 students is taken from the university.
(d) Find the probability that fewer than 3 of these students are members of the
university dance club and can dance the tango.
(2)
Downloaded by: brianryan1 |
Distribution of this document is illegal
2
,Question 1 continued.
(Total for Question 1 is 7 marks)
Downloaded by: brianryan1 |
Distribution of this document is illegal
3
,2. Marc took a random sample of 16 students from a school and for each student recorded
• the number of letters, x, in their last name
• the number of letters, y, in their first name
His results are shown in the scatter diagram on the next page.
(a) Describe the correlation between x and y.
(1)
Marc suggests that parents with long last names tend to give their children shorter first names.
(b) Using the scatter diagram comment on Marc’s suggestion, giving a reason for your
answer.
(1)
The results from Marc’s random sample of 16 observations are given in the table below.
x 3 6 8 7 5 3 11 3 4 5 4 9 7 10 6 6
y 7 7 4 4 6 8 5 5 8 4 7 4 5 5 6 3
(c) Use your calculator to find the product moment correlation coefficient between
x and y for these data.
(1)
(d) Test whether or not there is evidence of a negative correlation between the number
of letters in the last name and the number of letters in the first name.
You should
• state your hypotheses clearly
• use a 5% level of significance
(3)
Downloaded by: brianryan1 |
Distribution of this document is illegal
4
,Question 2 continued.
y
10
8
6
4
2
0
0 2 4 6 8 10 12 x
Downloaded by: brianryan1 |
Distribution of this document is illegal
5
,Question 2 continued.
Downloaded by: brianryan1 |
Distribution of this document is illegal
6
,Question 2 continued.
(Total for Question 2 is 6 marks)
Downloaded by: brianryan1 |
Distribution of this document is illegal
7
, 3. Stav is studying the large data set for September 2015
He codes the variable Daily Mean Pressure, x, using the formula y = x − 1010
The data for all 30 days from Hurn are summarised by
∑ y = 214 ∑ y2 = 5912
(a) State the units of the variable x
(1)
(b) Find the mean Daily Mean Pressure for these 30 days.
(2)
(c) Find the standard deviation of Daily Mean Pressure for these 30 days.
(3)
Stav knows that, in the UK, winds circulate
• in a clockwise direction around a region of high pressure
• in an anticlockwise direction around a region of low pressure
The table gives the Daily Mean Pressure for 3 locations from the large data set on 26/09/2015
Location Heathrow Hurn Leuchars
Daily Mean Pressure 1029 1028 1028
Cardinal Wind Direction
The Cardinal Wind Directions for these 3 locations on 26/09/2015 were, in random order,
W NE E
You may assume that these 3 locations were under a single region of pressure.
(d) Using your knowledge of the large data set, place each of these Cardinal Wind
Directions in the correct location in the table.
Give a reason for your answer.
(2)
Downloaded by: brianryan1 |
Distribution of this document is illegal
8
Statistics QP
,
, Please check the examination details below before entering your candidate information
Candidate surname Other names
Centre Number Candidate Number
Pearson Edexcel Level 3 GCE
Monday 18 October 2021 – Afternoon ▲ ▲
Mathematics
Advanced
Paper
reference 9MA0/31
PAPER 31: Statistics
You must have:
Candidates may use any calculator allowed by Pearson regulations.Total Marks
Mathematical
Calculators Formulae
must notand Statistical
have Tables
the facility for(Green),
symboliccalculator
algebra manipulation,
differentiation and integration, or have retrievable mathematical formulae
stored in them.
Instructions
•• IfUsepencil
black ink or ball‑point pen.
• centre number
is used for diagrams/sketches/graphs it must be dark (HB or B).
Fill in the boxes at the top of this page with your name,
• Answer
and candidate number.
all questions and ensure that your answers to parts of questions are
• Answer
clearly labelled.
the questions in the spaces provided
• You
– there may be more space than you need.
should show sufficient working to make your methods clear.
• Values
Answers without working may not gain full credit.
from statistical tables should be quoted in full. If a calculator is used instead of
• Inexact answers should be given to three significant figures unless otherwise stated.
tables the value should be given to an equivalent degree of accuracy.
Information
•• The
A booklet ‘Mathematical Formulae and Statistical Tables’ is provided.
total mark for this part of the examination is 50. There are 6 questions.
• –Theusemarks
this asfor eachas
a guide question are shown
to how much in spend
time to brackets
on each question.
• Read each question carefully before you start to answer it.
Advice
•• Check
Try to answer every question.
your answers if you have time at the end. Turn over
P68828A Downloaded by: brianryan1 |
©2021 Pearson Education Ltd.
Distribution of this document is illegal
A:1/1/1/1/1/
,1. (a) State one disadvantage of using quota sampling compared with simple random
sampling.
(1)
In a university 8% of students are members of the university dance club.
A random sample of 36 students is taken from the university.
The random variable X represents the number of these students who are members of the dance club.
(b) Using a suitable model for X, find
(i) P(X = 4)
(ii) P(X 7)
(3)
Only 40% of the university dance club members can dance the tango.
(c) Find the probability that a student is a member of the university dance club and can
dance the tango.
(1)
A random sample of 50 students is taken from the university.
(d) Find the probability that fewer than 3 of these students are members of the
university dance club and can dance the tango.
(2)
Downloaded by: brianryan1 |
Distribution of this document is illegal
2
,Question 1 continued.
(Total for Question 1 is 7 marks)
Downloaded by: brianryan1 |
Distribution of this document is illegal
3
,2. Marc took a random sample of 16 students from a school and for each student recorded
• the number of letters, x, in their last name
• the number of letters, y, in their first name
His results are shown in the scatter diagram on the next page.
(a) Describe the correlation between x and y.
(1)
Marc suggests that parents with long last names tend to give their children shorter first names.
(b) Using the scatter diagram comment on Marc’s suggestion, giving a reason for your
answer.
(1)
The results from Marc’s random sample of 16 observations are given in the table below.
x 3 6 8 7 5 3 11 3 4 5 4 9 7 10 6 6
y 7 7 4 4 6 8 5 5 8 4 7 4 5 5 6 3
(c) Use your calculator to find the product moment correlation coefficient between
x and y for these data.
(1)
(d) Test whether or not there is evidence of a negative correlation between the number
of letters in the last name and the number of letters in the first name.
You should
• state your hypotheses clearly
• use a 5% level of significance
(3)
Downloaded by: brianryan1 |
Distribution of this document is illegal
4
,Question 2 continued.
y
10
8
6
4
2
0
0 2 4 6 8 10 12 x
Downloaded by: brianryan1 |
Distribution of this document is illegal
5
,Question 2 continued.
Downloaded by: brianryan1 |
Distribution of this document is illegal
6
,Question 2 continued.
(Total for Question 2 is 6 marks)
Downloaded by: brianryan1 |
Distribution of this document is illegal
7
, 3. Stav is studying the large data set for September 2015
He codes the variable Daily Mean Pressure, x, using the formula y = x − 1010
The data for all 30 days from Hurn are summarised by
∑ y = 214 ∑ y2 = 5912
(a) State the units of the variable x
(1)
(b) Find the mean Daily Mean Pressure for these 30 days.
(2)
(c) Find the standard deviation of Daily Mean Pressure for these 30 days.
(3)
Stav knows that, in the UK, winds circulate
• in a clockwise direction around a region of high pressure
• in an anticlockwise direction around a region of low pressure
The table gives the Daily Mean Pressure for 3 locations from the large data set on 26/09/2015
Location Heathrow Hurn Leuchars
Daily Mean Pressure 1029 1028 1028
Cardinal Wind Direction
The Cardinal Wind Directions for these 3 locations on 26/09/2015 were, in random order,
W NE E
You may assume that these 3 locations were under a single region of pressure.
(d) Using your knowledge of the large data set, place each of these Cardinal Wind
Directions in the correct location in the table.
Give a reason for your answer.
(2)
Downloaded by: brianryan1 |
Distribution of this document is illegal
8
