Question

Find cov(X,Y) for the following data.

$\begin{array}{cc}X& Y\\ 4& 5\\ 6& 9\\ 8& 12\\ 10& 14\\ 12& 15\end{array}$

• A. 8
• B. 10
• C. 12
• D. 15

Answer 1

The correct option is B

10

$\begin{array}{ccccc}X& Y& X-\overline{X}& Y-\overline{Y}& (X-\overline{X})(Y-\overline{Y})\\ 4& 5& -4& -6& 24\\ 6& 9& -2& -2& 4\\ 8& 12& 0& 1& 0\\ 10& 14& 2& 3& 6\\ 12& 15& 4& 4& 16\\ & & & & \sum =50\end{array}$

$\overline{X}=\frac{\sum X}{N}=\frac{40}{5}=8$
$\overline{Y}=\frac{\sum Y}{N}=\frac{55}{5}=11$

$Cov(X,Y)=\frac{(X-\overline{X})(Y-\overline{Y})}{N}=\frac{50}{5}=10$