Question

on a separate piece of paper, complete the following table to calculate σ(x - x̄)(y - ȳ).
complete the table to calculate the sums

x	y	x - x̄	y - ȳ	(x - x̄)(y - ȳ)	(x - x̄)²	(y - ȳ)²
2	3
3	6
5	9
6	13
9	14
x̄ =	ȳ =			σ =	σ =	σ =

54
47
31
27
48

Explanation:

Step1: Calculate the means of x and y

$\bar{x}=\frac{2 + 3+5+6+9}{5}=\frac{25}{5}=5$
$\bar{y}=\frac{3 + 6+9+13+14}{5}=\frac{45}{5}=9$

Step2: Calculate the differences and products

For $(x = 2,y = 3)$:
$x-\bar{x}=2 - 5=-3$
$y-\bar{y}=3 - 9=-6$
$(x - \bar{x})(y - \bar{y})=(-3)\times(-6)=18$
$(x - \bar{x})^2=(-3)^2 = 9$
$(y - \bar{y})^2=(-6)^2 = 36$

For $(x = 3,y = 6)$:
$x-\bar{x}=3 - 5=-2$
$y-\bar{y}=6 - 9=-3$
$(x - \bar{x})(y - \bar{y})=(-2)\times(-3)=6$
$(x - \bar{x})^2=(-2)^2 = 4$
$(y - \bar{y})^2=(-3)^2 = 9$

For $(x = 5,y = 9)$:
$x-\bar{x}=5 - 5=0$
$y-\bar{y}=9 - 9=0$
$(x - \bar{x})(y - \bar{y})=0\times0 = 0$
$(x - \bar{x})^2=0^2 = 0$
$(y - \bar{y})^2=0^2 = 0$

For $(x = 6,y = 13)$:
$x-\bar{x}=6 - 5=1$
$y-\bar{y}=13 - 9=4$
$(x - \bar{x})(y - \bar{y})=1\times4 = 4$
$(x - \bar{x})^2=1^2 = 1$
$(y - \bar{y})^2=4^2 = 16$

For $(x = 9,y = 14)$:
$x-\bar{x}=9 - 5=4$
$y-\bar{y}=14 - 9=5$
$(x - \bar{x})(y - \bar{y})=4\times5 = 20$
$(x - \bar{x})^2=4^2 = 16$
$(y - \bar{y})^2=5^2 = 25$

Step3: Sum up the products

$\sum(x - \bar{x})(y - \bar{y})=18+6 + 0+4+20=48$

Answer:

48