Question

A doctor obtains the following information for the weights of seven mothers and their children from a maternity home for his research to know the relation between the weights of mother and weights of their children at the time of birth:

Weight of mother (kg)	59	72	66	64	77	66	60
Weight of child (kg)	2.5	3.4	3.1	2.7	2.8	2.3	3.0

Find rank correlation coefficient between the weights of mother and child.

Answer 1

Here, n = 7; x = Weight of mother;

y = Weight of child

R_x = Rank of weight of mother,

R_y = Rank of weight of child

The table for calculating the rank correlation coefficient is prepared as follows:

Rank correlation coefficient:

Here, observation 66 of x is repeated twice.
So CF is calculated as follows:

Now, \( r = 1 – \frac{6(Σd^2+CF)}{n(n^2−1)}\)

Putting n = 7, Σd² = 34.5 and CF = 0.5 in the formula,

Hence, the rank correlation coefficient between the weights of mother and child obtained is 0.38.