Quick question about Avg. and Std. Deviation relation.

[Mears]

Ok, if you have n items in a set and compute the standard deviation and then add a number x to one of the items in the original set and then recompute the average and std. deviation, you will find that the average is just the original average + x/n. Assuming the number x is positive, the std. deviation also increases. I'm trying to figure out if it increases by some non-arbitrary number as well. I'm starting to think that it doesn't. Yeah, I could say that it increases by the difference between the all the items in the set minus the new average, squared....minus the old standard deviation, but I'm wondering if there is some property that exists for this type of situation.

 

[Legendary]

Nope I believe you've got it. When you add something to a # in the set, you have to recalculate the Std Dev.