Answer to Question #133249 in Statistics and Probability for Jeyanthi s

Question

Ten competitors in a beauty contest were ranked by three judges as follows: Judges 2 3 4 5 6 7 A 6 10 3 10 2 7 8 9 10 9 B 5 8 9 7 1 2 7 8 9 1 C 4 9 7 10 2 3 9 7 3 9 7 7 Discuss which pair of judges have the nearest approach to common taste of beauty.

Answer 1

solution

we use ranked correlation coefficient to compare ranks given by different judges. Judges that give the most similar rankings will have the highest correlation coefficient.

The ranks given for the 10 participants are:

$Judge A: 6,10,3,10,2,7,8,9,10,9$

$Judge B: 5,8,9,7,1,2,7,8,9,1$

$Judge C: 4,9,7,10,2,3,9,7,3,9$

let

- $R_{AB}$ Be the correlation between judges A and B

- $R_{AC}$ Be the correlation between judges A and C

- $R_{BC}$ Be the correlation between judges B and C

$$R_{AB}=\frac{6}{N(N^2-1)}\sum(judgeA-judgeB)^2$$

$$R_{AC}=\frac{6}{N(N^2-1)}\sum(judgeA-judgeC)^2$$

$$R_{BC}=\frac{6}{N(N^2-1)}\sum(judgeB-judgeC)^2$$

Where N are the number of ranked individuals. Hence:

$$R_{AB} = \frac{6}{10(10^2-1)}* 143= 0.8667$$ $$R_{AC} = \frac{6}{10(10^2-1)}* 91= 0.5515$$ $$R_{BC} = \frac{6}{10(10^2-1)}* 122= 0.7394$$

The rank correlation coefficient is highest between judges A and B followed by judges B and C. Judges A and C have the lowest correlation coefficient.

Answer: Hence judges A and B have the nearest approach to common taste of beauty.