# Math Help - Standard deviation

1. ## Standard deviation

I'm interested in calculating standard deviation and have read your web site.
I hope to get your help:
If I have three groups of data A, B and C,
the mean values for A =a, B =b, and C =c,
the standard deviation(SD) for A =SD1, B =SD2, and C =SD3,
then what is the standard deviation for the average value of A, B and C, namely (A+B+C/3)?
Could you please tell me a formula to calculate their SD. If there are more groups of data?

Thank you very much.

2. Originally Posted by frkchen1438
I'm interested in calculating standard deviation and have read your web site.
I hope to get your help:
If I have three groups of data A, B and C,
the mean values for A =a, B =b, and C =c,
the standard deviation(SD) for A =SD1, B =SD2, and C =SD3,
then what is the standard deviation for the average value of A, B and C, namely (A+B+C/3)?
Could you please tell me a formula to calculate their SD. If there are more groups of data?

Thank you very much.
If you have data sets A, B, C, ... of sizes $N_A, N_B, N_C, ...$ and standard deviations of $\sigma_A, \sigma_B, \sigma_C, ...$, where sets A, B, C, ... all measure the same property, then
$\bar{\sigma} = \frac{\sqrt{N_A \sigma_A^2 + N_B \sigma_B^2 + N_C \sigma_C^2 + ...}}{N_A + N_B + N_C + ...}$

-Dan

3. Originally Posted by topsquark
If you have data sets A, B, C, ... of sizes $N_A, N_B, N_C, ...$ and standard deviations of $\sigma_A, \sigma_B, \sigma_C, ...$, where sets A, B, C, ... all measure the same property, then
$\bar{\sigma} = \frac{\sqrt{N_A \sigma_A^2 + N_B \sigma_B^2 + N_C \sigma_C^2 + ...}}{N_A + N_B + N_C + ...}$

-Dan
Thank you very much.
I have used your method to calculate my data, but the final standard deviations are much smaller than any standard deviation from every data sets. Is it ok? It is not in the range between max and min values?
New Question:
If I have two data sets A and B, with means a and b, and standard deviations SDa and SDb, respectively.
Now I need to calculate the ratio:
a/b, then what is the final standard deviation for the ratio?
Thank you again.

4. Originally Posted by topsquark
If you have data sets A, B, C, ... of sizes $N_A, N_B, N_C, ...$ and standard deviations of $\sigma_A, \sigma_B, \sigma_C, ...$, where sets A, B, C, ... all measure the same property, then
$\bar{\sigma} = \frac{\sqrt{N_A \sigma_A^2 + N_B \sigma_B^2 + N_C \sigma_C^2 + ...}}{N_A + N_B + N_C + ...}$

-Dan
Typo? The pooled variance formula gives:

$s_{pooled} = \sqrt{ \frac{(N_A-1) s_A^2 + (N_B-1) s_B^2 + (N_C-1) s_C^2 + ...}{(N_A-1) + (N_B-1) + (N_C-1) + ...}}$

RonL

5. Originally Posted by CaptainBlack
Typo? The pooled variance formula gives:

$s_{pooled} = \sqrt{ \frac{(N_A-1) s_A^2 + (N_B-1) s_B^2 + (N_C-1) s_C^2 + ...}{(N_A-1) + (N_B-1) + (N_C-1) + ...}}$

RonL
I used the wrong standard deviation formula again. (Sigh) Thanks for the spot.

-Dan

6. ## thank you

Originally Posted by CaptainBlack
Typo? The pooled variance formula gives:

$s_{pooled} = \sqrt{ \frac{(N_A-1) s_A^2 + (N_B-1) s_B^2 + (N_C-1) s_C^2 + ...}{(N_A-1) + (N_B-1) + (N_C-1) + ...}}$

RonL
Could you tell me where these formula come from? Thank you very much!
How about the standard deviation of a ratio of two mean values?
Thank you.
Frank

7. Originally Posted by frkchen1438
Could you tell me where these formula come from? Thank you very much!
How about the standard deviation of a ratio of two mean values?
Thank you.
Frank
The pooled variance formula you can find on wikipedia under pooled variance, and more hits than you will want if you type pooled variance into Google.

RonL

8. ## Yes, thanks

Originally Posted by CaptainBlack
The pooled variance formula you can find on wikipedia under pooled variance, and more hits than you will want if you type pooled variance into Google.

RonL
Yes, I have found a lot!
But I also hope to find the standard deviation of a ratio between two average values(in the case I have the standard deviation of each average)
Thanks.

Frank

9. Originally Posted by frkchen1438
Yes, I have found a lot!
But I also hope to find the standard deviation of a ratio between two average values(in the case I have the standard deviation of each average)
Thanks.

Frank
You will almost certainly end up with an approximation for this.

RonL

10. ## you mean use the same formula?

Originally Posted by CaptainBlack
You will almost certainly end up with an approximation for this.

RonL
Right? Why?
Thank you.