Standard Deviation Question

[Random]

I have a question in regards to standard deviation.

School is so great just to tell us just to use the calculator to get the standard deviation, but I was just wondering the actual formula, but I keep getting two 'versions' and I am not sure which should be used? Are they both lowercase sigma like I have written? When do you use them? THANK YOU!

\(\displaystyle \large\sigma = \sqrt {{{\sum {(x - \overline {x})^2} } } \over n} \cr\)

OR

\(\displaystyle \large\sigma = \sqrt {{{\sum {(x - \overline {x^})^2} } } \over {n - 1}} \cr\)

Random1

 

[JakeD]

I have a question in regards to standard deviation.

School is so great just to tell us just to use the calculator to get the standard deviation, but I was just wondering the actual formula, but I keep getting two 'versions' and I am not sure which should be used? Are they both lowercase sigma like I have written? When do you use them? THANK YOU!

\(\displaystyle \large\sigma = \sqrt {{{\sum {(x - \overline {x})^2} } } \over n} \cr\)

OR

\(\displaystyle \large\sigma = \sqrt {{{\sum {(x - \overline {x^})^2} } } \over {n - 1}} \cr\)

Random1

The first is for calculating the standard deviation over an entire population. The second is for estimating the standard deviation from a random sample . So for example, if you have data on the age of everyone in Rhode Island, use the first. But if you have only a random sample of ages of people from Rhode Island, use the second. See http://en.wikipedia.org/wiki/Standard_deviation for more.

 

[Random]

Thank you!