Question

Five students A, B, C, D and E have scored the following marks in Economics and Statistics. Find the rank coefficient of their marks.

$\begin{array}{ccc}Student& Statistics\left(S\right)& Economics\left(E\right)\\ A& 75& 90\\ B& 63& 60\\ C& 90& 88\\ D& 82& 80\\ E& 58& 75\end{array}$

• A. 0.4
• B. 0.6
• C. 0.7
• D. 0.8

Answer 1

The correct option is B

0.6

Convert the marks into corresponding ranks and calculate deviations.

$\begin{array}{ccccc}& S& E& D=S-E& D^2\\ A& 3& 1& 2& 4\\ B& 4& 5& -1& 1\\ C& 1& 2& -1& 1\\ D& 2& 3& -1& 1\\ E& 5& 4& 1& 1\\ & & & & \sum =8\end{array}$

$r_k=1-\frac{6\sum D_i^2}{n^3-n}=1-\frac{6\times 8}{125-5}=1-\frac{48}{120}=0.6$