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Question

The coefficient of rank correlation of the marks obtained by 10 students in two particular subjects was found to be 0.5. It was later discovered that the difference in ranks in two subjects obtained by one of the students was wrongly taken as 3 instead of 7. What should be the correct value of coefficient of rank correlation.


Solution

Given, rk = 0.5
N = 10

Now,
rk=1-6ΣD2N3-NSubstituting the given values in the formula we get,0.5=1-6ΣD21000-10or, 495=990-6ΣD2or, ΣD2=4956or, ΣD2=82.5Wrong ΣD2=82.5Correct ΣD2=82.5-32+72                    =122.5Substituting the value of correct ΣD2 in the formula for correlation coefficient:Correct Rank Correlation Coefficient ( rk) = 1-6×122.51000-10 rk=0.257

Hence, correct coefficient of rank correlation is 0.257.

Economics
Sandeep Garg (2019)
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