AS June 2025 Q1

EdexcelAS paperCurrent spec6 marksCorrelation

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. (4)

Each judge also gave a mark out of 20 for each singer’s vocal range.

Singer	\(A\)	\(B\)	\(C\)	\(D\)	\(E\)	\(F\)	\(G\)	\(H\)
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)

Mark scheme (a)

Scheme

Marks

	\(A\)	\(B\)	\(C\)	\(D\)	\(E\)	\(F\)	\(G\)	\(H\)
Judge 1	3	2	1	8	5	6	4	7
Judge 2	2	1	3	5	6	7	4	8

1.1b

\(\sum d^2 = 1 + 1 + 4 + 9 + 1 + 1 + 0 + 1\) [\(=18\)]

1.1b

\(r_s = 1 - \dfrac{6 \times \text{“}18\text{”}}{8 \times 63}\)

1.1b

\(= 0.7857\) = awrt 0.786

1.1b

(4)

Notes

M1: attempt to pair ranking by letter – at least 4 correct for each Judge

M1: attempt to find \(\sum d^2\) (some correct \(d\) values found and sum attempted)

M1: for using their \(\sum d^2\) in formula for \(r_s\) with \(n = 8\) (Independent of ranking)

A1: awrt 0.786 or exact fraction e.g. \(\dfrac{11}{14}\)

Mark scheme (b)

Scheme	Marks	AO
(Rank the marks and) for ties, use average ranks	B1	2.4
Calculate product moment correlation coefficient (using average ranks)	B1	2.4
	(2)
	(6 marks)

Notes

B1: explaining that average ranks need to be used. Must see examples or clear statement.

B1: explaining that the pmcc formula must be used on ranks. The “on ranks” may be implied or directly stated. Do not award if suggestion is simply to use pmcc on data.