Answer to Question #128955 in Statistics and Probability for Abdul Rehman

Question

Ten competitors in a beauty contest are ranked by three judges in the following order:-

First Judge

1 6 5 10 3 2 4 9 7 8

Second Judge

3 5 8 4 7 10 2 1 6 9

Third Judge

6 4 9 8 1 2 3 10 5 7

a. Use the rank correlation co efficient to discuss which pair of judges have the nearest approach to common tastes in beauty.

b. Could this problem be studied using correlation if yes then how? If not then why? Explain.

Answer 1

Here we calcuate three rank correlation coefficient:

r₁₂ beteen the ranks of judges I and II

r₂₃ beteen the ranks of judges II and III

r₁₃ beteen the ranks of judges I and III

r₁₂=1-(6$\sum$D²₁₂)/(N(N²-1))=1-(6*200)/(10*99)=-0.212

r₂₃=1-(6$\sum$D²₂₃)/(N(N²-1))=1-(6*214)/(10*99)=-0.297

r₁₃=1-(6$\sum$D²₁₃)/(N(N²-1))=1-(6*60)/(10*99)=0.636

The Judges I and III have nearest approach to common tastes in beauty where as the Judges II and III disagree the most

b. yes, to find out the nearest approach to common tastes in beauty judges, we should calculate the sets of correlation between the pairs of judges