Further Mathematics Paper 2, May/June. 2015

Question 6

Five finalists in a beauty pageant were ranked by two judges X and Y as shown in the table.


Judges

Anne

Linda

Susan

Rose

Erica

X

1

4

3

5

2

Y

3

2

4

5

1

Calculate the spearman’s rank correlation coefficient.

Observation

This question was reported to be very popular among the candidates and they performed very well in it. According to the report, majority of them were able to recall the appropriate formula, substituted the values and simplified correctly to obtain the expected result. However, a few of them were reported to have quoted the formula wrongly. They wrote  instead of 1 - . Others ranked the values again which was not necessary since we were told that they were ranks. Candidates were expected to obtain the following table


Rx

Ry

d

d2

1

3

-2

4

4

2

2

4

3

4

-1

1

5

5

0

0

2

1

1

1

 

 

 

Σd2 = 10

Thereafter, candidates would calculate the required coefficient using the formula
ρ = 1 - , where n = 5, Σd2 = 10. i.e. ρ = 1 -  = 0.5