Question

in order to use the defining formula for sample standard deviation, it is helpful to first calculate (x - x̅)² for each data value in the data set 1, 3, 5, 6, 7. use the values in the data set and the previously determined mean, x̅ = 4.4, to complete the following table.

x	x̅	x - x̅	(x - x̅)²
3	4.4		1.96
5	4.4	0.6
6	4.4		2.56
7	4.4	2.6

Explanation:

Step1: Calculate $x - \bar{x}$ for $x = 3$

$3 - 4.4=-1.4$

Step2: Calculate $(x - \bar{x})^2$ for $x = 5$

$0.6^2 = 0.36$

Step3: Calculate $x - \bar{x}$ for $x = 6$

$6 - 4.4 = 1.6$

Step4: Calculate $(x - \bar{x})^2$ for $x = 7$

$2.6^2=6.76$

Answer:

$x$	$\bar{x}$	$x - \bar{x}$	$(x - \bar{x})^2$
3	4.4	-1.4	1.96
5	4.4	0.6	0.36
6	4.4	1.6	2.56
7	4.4	2.6	6.76