AS October 2020 Q2

EdexcelAS paperCurrent spec9 marksCorrelation

2. Mary, Jahil and Dawn are judging the cakes in a village show. They have 5 features to consider and each feature is awarded up to 5 points. The total score the judges gave each cake are given in the table below.

Cake	\(A\)	\(B\)	\(C\)	\(D\)	\(E\)	\(F\)	\(G\)	\(H\)	\(I\)
Mary	19	17	23	10	21	15	12	8	14
Jahil	22	18	21	10	24	20	16	12	15
Dawn	9	11	6	18	9	15	13	20	13

(a) Calculate Spearman’s rank correlation coefficient between Mary’s scores and Jahil’s scores. (4)

(b) Calculate Spearman’s rank correlation coefficient between Jahil’s scores and Dawn’s scores. (3)

The judges discussed their interpretation of the points system and agreed that the first prize should go to cake \(C\).

(c) Explain how different interpretations of the points system could give rise to the results in part (a) and part (b). (2)

Mark scheme (a)

Scheme

Marks

Cake	\(A\)	\(B\)	\(C\)	\(D\)	\(E\)	\(F\)	\(G\)	\(H\)	\(I\)
Mary	3	4	1	8	2	5	7	9	6
Jahil	2	5	3	9	1	4	6	8	7

1.1b

\(\sum d^2 = 1 + 1 + 4 + 1 + 1 + 1 + 1 + 1 + 1\) [\(= 12\)]

1.1b

\(r_s = 1 - \dfrac{6 \times \text{“}12\text{”}}{9 \times 80}\)

1.1b

\(=\) 0.9

1.1b

(4)

Notes

1^st M1 an attempt to rank both – one row with at least 6 correct

2^nd dM1 (dep on an attempt at finding ranks) for an attempt to find \(\sum d^2\) (some correct \(d\) values found and sum attempted)

3^rd M1 for using their \(\sum d^2\) in formula for \(r_s\) with \(n = 9\) (Independent of ranking)

2^nd A1 for 0.9 or exact fraction e.g. \(\frac{9}{10}\)

NB No ranking leads to \(\sum d^2 = 81\) and \(r_s = 0.675\) and (a) M0M0M1A0 (b) M0M0A0

Mark scheme (b)

Scheme

Marks

Cake	\(A\)	\(B\)	\(C\)	\(D\)	\(E\)	\(F\)	\(G\)	\(H\)	\(I\)
Jahil	2	5	3	9	1	4	6	8	7
Dawn	7.5	6	9	2	7.5	3	4.5	1	4.5

1.1b

\(\mathrm{S}_{JJ} = 60 \quad \mathrm{S}_{DD} = 59 \quad \mathrm{S}_{JD} = 176 - \dfrac{45^2}{9} = -49\) (o.e.)

2.1

\(r_s = 0 - 0.823558\ldots\) awrt – 0.824

1.1b

(3)

Notes

1^st M1 for ranking Dawn’s results and dealing with tied ranks

2^nd M1 for selecting appropriate method to find \(r_s\) sight of 2 of these values or implied by ans

A1 for using their calculator to evaluate \(r_s\) allow awrt – 0.824

Mark scheme (c)

Scheme	Marks	AO
Mary and Jahil gave points for good features or high score is good Dawn gave points for poor features or low score is good	B1	2.4
Both strong correlation, M&J positive, J&D negative so agree	B1	2.4
	(2)
	(9 marks)

Notes

1^st B1 for idea that M and J gave points for good features but D for bad features

2^nd B1 for explaining that since both correlations are strong, one +, one – they agree