- #1

- 665

- 0

[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]?

- Thread starter amcavoy
- Start date

- #1

- 665

- 0

[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]?

- #2

- 184

- 0

possibly...

- #3

- 370

- 0

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

- #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.

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:

- 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

- Last Post

- Replies
- 2

- Views
- 4K

- Replies
- 5

- Views
- 2K