Range, and Standard Deviation?

http://en.wikipedia.org/wiki/Range_%28statistics%29

http://en.wikipedia.org/wiki/Arithmetic_mean

http://en.wikipedia.org/wiki/Standard_deviation#Basic_example_of_a_population_standard_deviation

The range is the difference between the biggest and smallest number in the set of numbers, and i was so bad with st. dev Senior year hahaha :[

It’s that time of the year again isn’t it? Homework already?

To calculate the standard deviation, compute the difference of each data point from the mean, and square the result. then average them and take the square root.
If you are confused as to why we square and then take the square root, it is because we need a positive number.

I’ll use your example.
The mean of the data set is (1+2+5+8+9+11)/6, which is 6.
now, take every point, and subtract 6 and square the result. This looks like this:
(1–6)^2= 25
(2–6)^2=16
(5–6)^2=1
(8–6)^2=4
(9–6)^2=9
(11–6)^2=25
Now, take all of the results and average them:
(25+16+1+4+9+25)/6=13.3333
Lastly, take the square root of that number, which gives you 3.651
But wait! That’s not all!

This method is not often used for smaller samples, such as yours.
Instead, in the second to last step (the averaging) one averages by the sample size-1, in this case, 5, so it looks like this:
(25+16+1+4+9+25)/(6–1)=16.
This gives us a final answer of 4. I would assume that you want this measurement, as it produces an unbiased estimator and is therefore ‘better’. I won’t go into further detail here, as that gets complicated plus, I’m not so sure that I really understand it.

What does your book say?

I guess this one wasn’t one of the odd questions.