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Re: [Phys-l] Basic statistics



On Nov 8, 2006, at 11:51 PM, Folkerts, Timothy J wrote:
One general comment. You say:

"We usually assume that the distribution of <x> is Gaussian and that the margin of error, on each side is equal to the standard deviation, s, obtained from measurements. "

Do you mean the distribution of the individual values of x is Gaussian, or do you mean that the distribution the actual averages is Gaussian (i.e. you measured <x> several times and the distributions of those values of <x> follow a Gaussian distribution)? The "margin of error" for the distribution of x is s, but the "margin of error" of <x> is generally taken as s/(N^0.5) wher N is the number of values averaged to find <x>.

I think you mean the distribution of x(i) itself, but this distinction needs to be clear throughout the discussion.

Suppose x was measured 9 times and <x>=19.3. The data point is plotted as 19.3. Suppose that s, based on nine results, was 1.2. Should the error bar be 1.2 or should it be 0.4, as indicated by Tim's formula? I think it should be 0.4 because 19.3 is the mean value. I will read my draft again and see what should be changed. But first let us agree that the margin of error should be 0.4 and not 1.2. Too bad I gave away my old lab manuals. What do lab manuals tell students to plot?
P.S.
Thanks John, the &mu; did the job. The corrected webpage,

http://blake.montclair.edu/~kowalskil/basicstat.html

now shows the Greek symbol. But most references I saw, including yours, suggested &micro; which did not work for me. Was "micro" replaced by "mu" recently?

Ludwik Kowalski
Let the perfect not be the enemy of the good.