Question

I need help with standard deviation involving decimals

Answer 1

Welcome to Open Study @rchavis1 :D

Answer 2

What is your question?

Answer 3

Well, we can always start with the definition of the standard deviation:\[\sigma =\sqrt{<x ^{2}>-<x>^{2}}\]where σ is the standard deviation; <x^2> is the mean (average) of all the x^2 and <x> is the mean of all x.

So let's do an example. A class of 5 students has the following test results: 95, 90, 83, 79, and 78. What is <x^2>? It is:\[<x ^{2}>=\frac{ 95^{2}+90^{2}+83^{2}+79^{2}+78^{2} }{5 }=7267.8\] What is <x>^2? It is the average of those five test results squared:\[<x>^{2}=\left( \frac{ 95+90+83+79+78 }{ 5 } \right)^{2}=85^{2}=7225\]Now our equation is as follows:\[\sigma =\sqrt{7267.8-7225}=\sqrt{42.8}=6.5\]Hopefully this will give you some help.