Answer to Question #150259 in Statistics and Probability for gemma

Question

(b) Nine competitors in a beauty contest were given the following marks by three judges:

Competitors
Judges 1 2 3 4 5 6 7 8 9
A 56 54 65 69 72 74 77 88 54
B 65 78 62 74 55 82 66 64 82
C 64 79 68 71 82 73 81 84 81

Using the knowledge of ranking data, describe the pair of judges with nearest approach and the furthest approach to common tastes of beauty

Answer 1

Rank the marks:

judges 1   2   3   4   5   6   7   8   9

A 2   9   1   3   4   5   6   7   8

B 5   3   8   1   7   4   2   6   9

C 1   3   4   6   2   7   9   5   8

Calculate sum of squares of the differences:

$D(RA, RB) = \sum_{i} d^2(RA_i, RB_i)=126$

D(RA, RC) = 76

D(RB, RC) = 142

Hence, judges A and C with nearset approach

judges B and C with furthest approach