Spearman's rank correlation coefficientEdexcel International A Level Further Maths: Mind map

Exam questions on Spearman's rank correlation coefficient

1. Two judges, X and Y, each rank six dancers A to F, with rank 1 for the best. Judge X ranks them A, B, C, D, E, F in that order, so A is 1st and F is 6th. Judge Y gives A rank 3, B rank 1, C rank 2, D rank 5, E rank 4 and F rank 6.
   Interpret the value of the coefficient for the two judges.2 marks
2. A teacher ranks eight students A to H from the highest mark (rank 1) to the lowest in maths, and again in physics. The maths ranks of A to H are 1 to 8 respectively. The physics ranks of A to H are 3, 1, 2, 5, 4, 8, 6 and 7 respectively.
   A second teacher gives the physics ranks with rank 1 for the lowest mark instead of the highest, and leaves the maths ranks unchanged. State the new value of the coefficient, with a reason.2 marks
3. A café owner compares seven coffee blends A to G. The prices per kilogram, in pounds, are A 12, B 18, C 15, D 22, E 9, F 25 and G 20. The customer rating scores out of 10 are A 6.1, B 7.0, C 5.8, D 8.2, E 4.9, F 7.9 and G 7.4.
   Rank the blends by price and by rating, and calculate Spearman's rank correlation coefficient.3 marks