Question

Obtain the rank correlation coefficient of the
following data (in lacs) & interpret the result
obtained

Expenditure on advertisement
25 28 21 30 32 34 27 25 26 28 21

Profit
16 15 17 23 20 18 21 25 18 20 22
​

Answer 1

Given : Expenditure on advertisement and Profit

Expenditure on

advertisement E    Profit  P

25                        16

28                        15

21                         17

30                        23

32                      20

34                        18

27                         21

25                       25

26                        18

28                        20

21                         22

To Find : the rank correlation coefficient

Solution:

Re = rank of Expenditure

Rp =  rank of profit

di =  Re - Rp

As in E  21 has rank 1 and 2 so both are assigned (1 + 2)/2 = 1.5

E      P     Re   Rp     di     di²  

25 16 3.5 2 1.5 2.25

28 15 7 1 6 36

21 17 1.5 3 -1.5 2.25

30 23 9 10 -1 1

32 20 10 6.5 3.5 12.25

34 18 11 4.5 6.5 42.25

27 21 6 8 -2 4

25 25 3.5 11 -7.5 56.25

26 18 5 4.5 0.5 0.25

28 20 8 6.5 1.5 2.25

21 22 1.5 9 -7.5 56.25

     215

 ∑ (di)² = 215

 n = 11

rank correlation coefficient    = 1   - 6  ∑ (di)² / (n(n² - 1))

= 1  - 6( 215 / 11 ( 11² - 1))

= 1 - 0.977

= 0.023

Learn More:

What is the rectified rank correlation coefficient

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