Question

use the table below to compute $(x - \bar{x})^2$, using the previously determined value $\bar{x}=10.3$.

representative age	$x - \bar{x}$	$(x - \bar{x})^2$
7.0	$7.0 - 10.3=-3.3$	$(-3.3)^2=square$
10.0	$10.0 - 10.3=-0.3$	$(-0.3)^2=square$
13.5	$13.5 - 10.3 = 3.2$	$(3.2)^2=square$
17.0	$17.0 - 10.3 = 6.7$	$(6.7)^2=square$

calculate the sum $sum(x - \bar{x})^2$.
$sum(x - \bar{x})^2=square$

Explanation:

Step1: Calculate $(-3.3)^2$

$(-3.3)^2=(-3.3)\times(-3.3) = 10.89$

Step2: Calculate $(-0.3)^2$

$(-0.3)^2=(-0.3)\times(-0.3)=0.09$

Step3: Calculate $(3.2)^2$

$(3.2)^2 = 3.2\times3.2=10.24$

Step4: Calculate $(6.7)^2$

$(6.7)^2=6.7\times6.7 = 44.89$

Step5: Calculate the sum $\sum(x - \bar{x})^2$

$\sum(x - \bar{x})^2=39.69+10.89 + 0.09+10.24+44.89=105.8$

Answer:

For $(-3.3)^2$: $10.89$
For $(-0.3)^2$: $0.09$
For $(3.2)^2$: $10.24$
For $(6.7)^2$: $44.89$
For $\sum(x - \bar{x})^2$: $105.8$