What does SIGMA mean in mathematics?

[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?

 

[John Creighto]

In mathematics, the Greek letter Sigma (Σ) is often used to represent the summation operator. When you see Σ in a mathematical expression, it typically indicates that you should sum a series of numbers or terms. The letter Sigma is followed by an expression that specifies the terms to be summed, and the summation is performed over a specified range or set of values.

For example, the expression Σn from n = 1 to 5 represents the sum of the numbers 1, 2, 3, 4, and 5:

Σn from n = 1 to 5 = 1 + 2 + 3 + 4 + 5 = 15

You can use Σ to represent more complex summations involving variables, sequences, or other mathematical expressions. It is a concise way to express the idea of adding up a series of terms or values.

 

[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.

 

[vokurka]

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