Mumbai University > Mechanical Engineering > Sem 4 > Applied Mathematics IV

Marks: 6M

Year: May 2014

Spearman's rank correlation co-efficient:

Here , $m_1=2\ ;\ m_2=3;n=6$

$$\mathrm{\therefore } R = 1 - \frac{6}{n\left(n^2-1\right)}\ \left\{\ \sum{d^2_i+\ \frac{1}{12}\ [(}m^3_1-\ m_1\right)+(m^3_2-\ m_2)]\}$$ $$ = 1 - \frac{6}{6\left(6^2-1\right)}\ \left\{\ \ 13.5+\ \frac{1}{12}(2^3-\ 2\right)+(3^3-\ 3)]\}$$ $$ = 1 - \frac{1}{35}\ \left\{\ 13.5+\ \frac{1}{12}\left[6+24\right]\right\}$$ $$ = 1 - \frac{1}{35}\left\{\ 13.5+2.5\right\}$$ $$= 0.5429$$

Spearman's rank correlation co-efficient (R) = 0.5429