ANSWER
426.6
EXPLANATION
We want to find the Standard deviation of the data given.
To do this, we will use the formula:
[tex]\begin{gathered} SD=\sqrt{\frac{\sum (x\text{ - }\mu)^2}{n}} \\ \text{where }\mu\text{ = mean of the data} \end{gathered}[/tex]
Let us first find the mean:
[tex]\begin{gathered} \mu\text{ = }\frac{3990\text{ + 412}0\text{ + 3500 + 3100 + }2990\text{ + 3810 + 4120 + 4020 }}{8} \\ \mu\text{ = }\frac{29560}{8} \\ \mu\text{ = 3695} \end{gathered}[/tex]
Now, we will subtract the mean from each number in the set of data(x - u):
3990 - 3695 = 295
4120 - 3695 = 425
3500 - 3695 = -195
3100 - 3695 = -595
2990 - 3695 = -705
3810 - 3695 = 115
4120 - 3695 = 425
4020 - 3695 = 325
Now, square each of those values and add them:
[tex]\begin{gathered} \sum (x\text{ - }\mu)^2=(295)^2+(425)^2+(-195)^2+(-595)^2+(-705)^2+(115)^2+(425)^2+(325)^2 \\ \sum (x\text{ - }\mu)^2\text{ = 87025 + 180625 + 38025 + 354025 + 497025 + 13225 + 180625 + 105625} \\ \sum (x\text{ - }\mu)^2\text{ = }1456200 \end{gathered}[/tex]
Now, divide by the number of data points (8):
[tex]\begin{gathered} \frac{\sum (x\text{ - }\mu)^2}{n}\text{ = }\frac{1456200}{8} \\ \frac{\sum (x\text{ - }\mu)^2}{n}\text{ = }182025 \end{gathered}[/tex]
Now, find the square root:
[tex]\begin{gathered} SD\text{ = }\sqrt{\frac{\sum (x\text{ - }\mu)^2}{n}}\text{ = }\sqrt{182025} \\ SD\text{ = 426.6} \end{gathered}[/tex]
That is the answer.
