Question

consider the following data: 5 8 2 1 7 1 determine the standard deviation by filling in the table as part of your calculation.

x	$\bar{x}$	$x - \bar{x}$	$(x - \bar{x})^2$
5	4	1	1
8	4	4	16
2	4	-2	4
1	4
7	4
1	4

a. 8
b. $sqrt{8} approx 2.83$
c. 2
d. $sqrt{2} approx 1.41$

Explanation:

Step1: Calculate remaining $(x - \bar{x})$ values

For $x = 1$, $\bar{x}=4$, so $x-\bar{x}=1 - 4=-3$.
For $x = 7$, $\bar{x}=4$, so $x-\bar{x}=7 - 4 = 3$.
For $x = 1$, $\bar{x}=4$, so $x-\bar{x}=1 - 4=-3$.

Step2: Calculate remaining $(x - \bar{x})^2$ values

For $x-\bar{x}=-3$, $(x - \bar{x})^2=(-3)^2 = 9$.
For $x-\bar{x}=3$, $(x - \bar{x})^2=3^2 = 9$.
For $x-\bar{x}=-3$, $(x - \bar{x})^2=(-3)^2 = 9$.

Step3: Calculate the sum of $(x - \bar{x})^2$ values

$1+16 + 4+9+9+9=48$.

Step4: Calculate the variance

The variance $s^{2}=\frac{\sum(x - \bar{x})^2}{n}$, where $n = 6$. So $s^{2}=\frac{48}{6}=8$.

Step5: Calculate the standard deviation

The standard deviation $s=\sqrt{s^{2}}=\sqrt{8}\approx2.83$.

Answer:

b. $\sqrt{8}\approx2.83$