Question

The sum of squares of differences of ranks of observation (x, y) is 192 and the coefficient of rank

correlation is -0.6. Find the number of observations.​

Answer 1

Answer:

The rank correlation coefficient r between the two variables x, y is given by the formula;

r = 1 -{6 sigma(d^2)/n(n^(2) - 1)} … ..(1) , where d is the difference between ranks of the corresponding values of x, y and n is the no. of pairs of x & y .

Here in the present case given r = (2/3) and sigma(d^2) = 28 . Putting these values in (1), we get an equation in n as ; n^3 - n - 504 = 0 or

(n - 8)(n^2 +8n +63) = 0 ==> n = 8 . Note that other bracket expression gives complex values for n . Hence n= 8 is the answer.

Step-by-step explanation: