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May 2025 Edexcel: AS Level Further Mathematics 8FM0/24 (Option G only) Further Statistics 2 – Merged Question Paper & Mark Scheme

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May 2025 Edexcel: AS Level Further Mathematics 8FM0/24 (Option G only) Further Statistics 2 – Merged Question Paper & Mark Scheme 1. In a singing competition, two judges ranked the vocal quality of each of 8 singers. The singers are labelled A to H and the table below shows the ranks given by each judge. Rank 1 2 3 4 5 6 7 8 Judge 1 C B A G E F H D Judge 2 B A C G D E F H (a) Calculate the Spearman’s rank correlation coefficient between the judges’ ranks. Each judge also gave a mark out of 20 for each singer’s vocal range. (4) Singer A B C D E F G H Judge 11 7 13 6 Judge 9 8 12 8 (b) Without carrying out any further calculations, explain how the Spearman’s rank correlation coefficient between the judges’ marks for vocal range should be calculated. 2 (2) ■■■■ DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 1 continued ■■■■ (Total for Question 1 is 6 marks) 3 Turn over DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 2. The graph of the probability density function f(x) of the continuous uniform random variable X is shown below. f(x) 0.3 0.1 –4 –3 –2 –1 0 1 2 3 4 x (a) Write down the value of P(X = 1) (b) Find E(X) (c) Find Var(X) (d) Sketch the cumulative distribution function of X for –3 x 2 You should label any points where the sketch touches or crosses the coordinate axes. (e) Find P(X 2 > 1.96) 4 (1) (1) (1) (3) (3) ■■■■ DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 2 continued ■ ■ ■ ■ 5 Turn over DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 2 continued 6 ■ ■ ■ ■ DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA Question 2 continued ■■■■ (Total for Question 2 is 9 marks) 7 Turn over DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA DO NOT WRITE IN THIS AREA 3. Dina is investigating the relationship between a marathon runner’s body mass index (BMI), x kgm–2 , and the runner’s average speed when running a marathon, vms –1 She collects data from 20 marathon runners. Some summary statistics are given below. x 19.8 v  5.2 xv  2056.63 Sxx 15.78 Svv  0.94 (a) Show that Sxv = –2.57 (b) Find the value of the product moment correlation coefficient between v and x (c) Use a suitable test, with a 5% level of significance, to assess whether or not there is evidence of a negative correlation between BMI and average speed. State the hypotheses and the critical value used. (d) Find the equation of the regression line of v on x in the form

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May 2025 Edexcel: AS Level Further Mathematics
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May 2025 Edexcel: AS Level Further Mathematics
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May 2025 Edexcel: AS Level Further Mathematics

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May 2025 Edexcel: AS Level Further
Mathematics 8FM0/24 (Option G only)
Further Statistics 2 – Merged Question
Paper & Mark Scheme




Afternoon

Further Mathematics 🟐 🟐

Advanced Subsidiary
Further Mathematics options
24: Further Statistics 2
(Part of option G only)




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-point pen.


If pencil is used for diagrams/sketches/graphs it must be dark (HB or B).
Fill in the boxes
andatcandidate
the top ofnumber.
this page with your name,

centre number
Answer all questions and ensure that your answers to parts of questions are clearly labelled.
• –Answer the questions
there may in thethan
be more space spaces
youprovided
need.

• You should show sufficient working to make your methods clear. Answers 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.
Information
•• A booklet ‘Mathematical Formulae and Statistical Tables’ is provided.


The total mark for this part of the examination is 40. There are 4 questions.
The
– usemarks
this asfor each as
a guide question
to how are
muchshown
timeintobrackets
spend on each question.


Advice
Read each question carefully before you start to answer it.
•• Try to answer every question.
Check your answers if you have time at the end. Turn over


P76374A
©2025 Pearson Education Ltd.
Y:1/1/1/

,1. In a singing competition, two judges ranked the vocal quality of each of 8 singers.

The singers are labelled A to H and the table below shows the ranks given by




DO NOT WRITE IN THIS AREA
each judge.


Rank 1 2 3 4 5 6 7 8

Judge 1 C B A G E F H D

Judge 2 B A C G D E F H


(a) Calculate the Spearman’s rank correlation coefficient between the judges’ ranks.
(4)
Each judge also gave a mark out of 20 for each singer’s vocal range.


Singer A B C D E F G H




DO NOT WRITE IN THIS AREA
Judge 1 18 13 16 12 11 7 13 6

Judge 2 15 17 14 14 9 8 12 8


(b) Without carrying out any further calculations, explain how the Spearman’s
rank correlation coefficient between the judges’ marks for vocal range should
be calculated.
(2)




DO NOT WRITE IN THIS AREA




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 6 marks)

3

■■■■ Turn over
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