Question

the marks secured by recruits in the selection test X and in the proficiency test Y are given below
.
serial No: 1 2 3 4 5 6 7 8 9
X: 10 15 12 17 13 16 24 14 22
Y: 30 42 45 46 33 34 40 35 39

calculate the rank correlation coefficient.​

Answer 1

Answer:

the rank correlation coefficient for this data set is 0.117, which indicates a weak positive correlation between X and Y.

Step-by-step explanation:

To calculate the rank correlation coefficient, we need to first assign ranks to the values in both X and Y. We can use either the average rank or the minimum rank for ties. Here, we will use the average rank for ties.

Serial No: 1 2 3 4 5 6 7 8 9

X: 10 15 12 17 13 16 24 14 22

X Rank: 1 5 3 8 4 7 9 6 2

Serial No: 1 2 3 4 5 6 7 8 9

Y: 30 42 45 46 33 34 40 35 39

Y Rank: 2 7 8 9 4 5 6 3 1

Now, we can calculate the rank correlation coefficient using the formula:

r = 1 - (6ΣD^2)/(n(n^2-1))

where

D = difference in ranks

n = number of pairs of ranks

ΣD^2 = sum of squared differences in ranks

ΣD^2 = (1-2)^2 + (5-7)^2 + (3-8)^2 + (8-9)^2 + (4-5)^2 + (7-6)^2 + (9-3)^2 + (6-1)^2 + (2-4)^2

ΣD^2 = 106

n = 9

r = 1 - (6ΣD^2)/(n(n^2-1))

r = 1 - (6106)/(9(9^2-1))

r = 1 - (636/720)

r = 0.117

Therefore, the rank correlation coefficient for this data set is 0.117, which indicates a weak positive correlation between X and Y.
for more questions on rank correlation coefficient

https://brainly.in/question/29073289

#SPJ3