Question

As the manager of a company, you want to put together a team of two people who have dissimilar strengths. Three people X,Y and Z were asked to rate themselves on the skills of problem-solving (P), coordination (C), numeracy (N) and man-management (M). Their responses are tabulated below.
$\begin{array}{cccc}Skills& X& Y& Z\\ P& 10& 6& 8\\ C& 7& 8& 7\\ M& 5& 9& 10\\ N& 8& 7& 6\end{array}$

Which two of them would you choose to make a team based on their responses?

• A. X and Y
• B. Y and Z
• C. X and Z
• D. Cannot be concluded

Answer 1

The correct option is A

X and Y

Convert the ratings of X and Y to corresponding ranks and calculate deviations.

$\begin{array}{ccccc}Contestants& X& Y& D_i=X-Y& D_i^2\\ P& 1& 4& -3& 9\\ C& 3& 2& 1& 1\\ M& 4& 1& 3& 9\\ N& 2& 3& -1& 1\\ & & & & \sum =20\end{array}$

$r_k=1-\frac{6\sum D_i^2}{n^3-n}=1-\frac{6\times 20}{64-4}=1-\frac{120}{60}=-1$

The correlation of -1 indicates that the strengths of X and Y are as diverse as it can get. Hence, the team should be formed with X and Y.