# What is SIGMA MEAN ?

1. Jul 29, 2009

### vokurka

In my lab I measure some chemical data. Output from the software I use contain also some stats, like the mean value, standard deviation and some number called SIGMA MEAN. My typical dataset looks like this:

sample MgO Al2O3
a 5,307872109 7,45113642
b 8,496074587 9,182072932
c 1,413995015 7,488017765
d 5,241196501 12,15347965
e 1,592772949 7,863316958
f 0,518347063 4,050451192
g 1,117824945 5,952661741

Mean value: 3,384011881 7,734448094
Sigma: 2,992231593 2,53402361
Sigma mean: 1,130957237 0,957770898

I know what is mean value and standard deviation sigma, but I never heard about sigma mean. It is always smaller than sigma and it seems to depend on sigma. Please do somebody know what it is Sigma mean?

2. Jul 29, 2009

### John Creighto

My guess, is sigma is the standard deviation in each sample, while sigma mean is your uncertainty in the mean. You can't measure the mean exactly because you have finite data so there will be some uncertainty in your estimate of the mean.

3. Aug 8, 2009

### Mapes

John Creighto is correct; this parameter is the standard error (the sample deviation divided by the square root of the number of samples), which represents the uncertainty of the mean.

4. Aug 10, 2009

### vokurka

Thank you very much Mapes and John Creighto for help, now it is absolutely clear to me.