In a skating competition the judges gave the five competitors the following marks. Calculate a coefficient of rank correlation.
Competitors A B C D E
1st judge 5.7 5.8 5.9 5.6 5.5
2nd judge 5.6 5.7 6.0 5.5 5.8

0.4

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0.56

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0.67

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0.89

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Solution

The correct option is A $0.4$

Competition

$1 s t$ Judge

Rank

$2 n d$ Judge

Rank

$| d |$

$d^{2}$

A

B

C

D

E

5.7

5.8

5.9

5.6

5.5

3

2

1

4

5

5.6

5.7

6.0

5.5

5.8

4

3

1

5

2

1

1

0

1

3

1

1

0

1

9

$n = 5, \sum d^{2} = 12$

$r = 1 - \frac{6 \sum d^{2}}{n (n^{2} - 1)} = 1 - \frac{6 \times 12}{5 (5^{2} - 1)} = 1 - \frac{72}{240} = 0.44$

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In a skating competition the judges gave the five competitors the following marks. Calculate a coefficient of rank correlation.CompetitorsABCDE1st judge5.75.85.95.65.52nd judge5.65.76.05.55.8

The correct option is A 0.4 Competition 1st Judge Rank 2nd Judge Rank |d| d2 A B C D E 5.7 5.8 5.9 5.6 5.5 3 2 1 4 5 5.6 5.7 6.0 5.5 5.8 4 3 1 5 2 1 1 0 1 3 1 1 0 1 9 n=5,∑d2=12 r=1−6∑d2n(n2−1)=1−6×125(52−1)=1−72240=0.44

In a skating competition the judges gave the five competitors the following marks. Calculate a coefficient of rank correlation.
Competitors A B C D E
1st judge 5.7 5.8 5.9 5.6 5.5
2nd judge 5.6 5.7 6.0 5.5 5.8