Question

The following table shows the ages of people and the corresponding weight
Age(year) 25 40 38 53 40 32 48 59 45 36
Weight (Kgs) 43 52 48 61 63 40 67 72 47 41
Calculate the Spearman’s Rank correlation coefficient and comment.

Answer 1

Assigning ranks to the given observation values we get,

Age(year) 25 40 38 53 40 32 48 59 45 36

Rank - 1 5.5 4 9 5.5 2 8 10 7 3

Weight (Kgs) 43 52 48 61 63 40 67 72 47 41

Rank- 3 6 5 7 9 1 8 10 4 2

Using the Spearman's Rank correlation coefficient as follows-

$\rho=1- \frac {6* \sum d_i^2}{n(n^2-1)}$

Where,

$\rho$ = Spearman's Rank correlation coefficient

d_i = difference between the two ranks of each observation

n = number of observations

substituting the values in the above equation we get,

$\rho = 1 - \frac {6*(2^2+0.5^2+1^2+2^2+3.5^2+1^2+0^2+0^2+3^2+5^2)}{10*(10^2-1)}=1-\frac{6*56.5}{990}$

Hence,

$\rho = 0.657575$

Since the value of $\rho$ is not negative we can say that there is a positive correlation between the various ages of people and their corresponding weights and its value is 0.657575