Question

Given below is the percentage of marks secured by 5 students in Economics and Statistics.

$\begin{array}{cccccc}\text{Students}& \text{A}& \text{B}& \text{C}& \text{D}& \text{E}\\ \text{Marks in Economics}& 60& 48& 49& 50& 55\\ \text{Marks in Statistics}& 85& 60& 55& 65& 75\end{array}$
Calculate the coefficient of rank correlation.

Answer 1

Calculation of Rank correlation

$\begin{array}{cccccc}\text{Marks in Economics}& R_1& \text{Marks in Statistics}& R_2& D=R_1-R_2& D^2\\ 60& 1& 85& 1& 0& 0\\ 48& 5& 60& 4& +1& 1\\ 49& 4& 55& 5& -1& 1\\ 50& 3& 65& 3& 0& 0\\ 55& 2& 75& 2& 0& 0\\ & & & & & \sum D^2=2\end{array}$

Here, $N=5$ and $\sum D^2=2$
$\therefore R_k=1-\frac{6\sum D^2}{N^3-N}=1-\frac{6\times 2}{5^3-5}=1-\frac{12}{120}$
$=1-0.1=+0.90$

$\therefore R_k=+0.90$

It indicates that there is high degree of correlation between the marks in Economics and Statistics.