Standard Deviation

  • Thread starter amcavoy
  • Start date
  • #1
665
0
For sets X and Y, is it true that

[tex]s_{XY}=s_{X}\overline{Y}+s_{Y}\overline{X},[/tex]​

where [tex]s[/tex] represents the standard deviation and [tex]XY[/tex] is the set containing [tex]x_{i}y_{i}[/tex]?
 

Answers and Replies

  • #3
370
0
First off, I assume you mean sample deviation? Standard deviation is a constant.

I doubt the result is true in general. However, there may be a specific case where the formula holds.

Do you have any idea what X and Y might be distributed as? Where does the problem arise?
 
  • #4
matt grime
Science Advisor
Homework Helper
9,395
3
What are X and Y, and what does XY really mean? How can x_iy_i make sense, since this will completely depend on how one labels elements of the sets (apparently they're sets) X and Y? It also presupposes that |X|=|Y| too.
 
  • #5
Simfish
Gold Member
818
2
Hi there. Remember me? :)

I think it means that the standard deviation of the union of X and Y is equal to the standard deviation of x * the mean of Y + the standard deviation of y * the mean of X.

Uggh I don't know how to prove those - have to go to some statistics textbooks...

Anyways, if Y mean = 100 and Y SD = 0, and X mean = 0 and X SD = 0, then the formula would compute a combined SD of 0. But then your combined sample has both elements of 0 and 100, and it must have a standard deviation. So the formula is not universally true.
 
Last edited:

Related Threads on Standard Deviation

  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
5
Views
1K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
4
Views
688
Replies
11
Views
3K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
1
Views
2K
Replies
2
Views
4K
Replies
5
Views
2K
Top