What is the correlation factor (C.F) in the rank correlation coefficient?
A. \[C.F=\sum{\left( {{m}^{2}}-1 \right)}\]
B. \[C.F=\sum{\left( {{m}^{2}}+1 \right)}\]
C. \[C.F=\sum{{{m}^{2}}\left( {{m}^{2}}-1 \right)}\]
D. \[C.F=\sum{m\left( {{m}^{2}}-1 \right)}\]

Hint: In this problem, we can see about correlation factor (C.F) in the rank correlation coefficient. Here we should know that in mathematics, correlation in which there are ties in ranks, we will take average rank in all of the ties and then total correction factor is added to the summation of squares of difference in ranks. We can now see about the formula and find the correct formula for the given question among the given options.

Complete step by step answer:
Here we have to find the correlation factor (C.F) in the rank correlation coefficient among the given options.
We should know that in mathematics, correlation in which there are ties in ranks, we will take average rank in all of the ties and then total correction factor is added to the summation of squares of difference in ranks.
The correlation in the rank correlation coefficient is given by
\[\Rightarrow C.F=\sum{m\left( {{m}^{2}}-1 \right)}\]
Where, m is the number of times the data repeats.
Therefore, the correlation factor (C.F) in the rank correlation coefficient is option D. \[C.F=\sum{m\left( {{m}^{2}}-1 \right)}\].

So, the correct answer is “Option D”.

Note: We should always remember the concept of correlation factor where in mathematics, correlation in which there are ties in ranks, we will take average rank in all of the ties and then total correction factor is added to the summation of squares of difference in ranks. The formula for it is \[C.F=\sum{m\left( {{m}^{2}}-1 \right)}\].