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The rankings of ten students in two subjects, Mathematics and Statistics, are as follows.

Mathematics

Statistics

3

6

5

4

8

9

4

8

7

1

10

2

2

3

1

10

6

5

9

7


The coefficient of rank correlation is:
1. -0.3
2. 0.3
3. 0.1
4. -0.1

1 Answer

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Best answer
Correct Answer - Option 1 : -0.3

Calculation

The coefficient of rank correlation = 1 – 6∑d2/n(n2 – 1)

D = r1 – r2

r1, r2 ------ are ranks

Mathematics (r1)

Statistics (r2)

d = Ir1 – r2I

d2

3

6

3

9

5

4

1

1

8

9

1

1

4

8

4

16

7

1

6

36

10

2

8

84

2

3

1

1

1

10

9

81

6

5

1

1

9

7

2

4

Total

10

 

∑d2 = 214

According to spearman’s rank correlation coefficient ρ = 1 – 6∑d2/n(n2 – 1)

⇒ 1 – 6 × 214/10(100 – 1)

⇒ 1 – 6 × 214/990

⇒ 1 – 1.297

The value of rank correlation is approx. – 0.3

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