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Re: [Phys-l] projectile motion lab

The book to which I referred does that, quite clearly and here it is: [UC for italics]

4.4 The SD of the Mean

If X1 ....., Xn are the results of N measurements of the same quantity X, then, as we have seen, our best estimate of the quantity X is their mean, X bar. We have also seen that the SD sigma x characterizes the average uncertainty of the separate measurements X1, .... Xn. However, our answer X best = X bar represents a judicious combination of all N measurements, and there is every reason to think it will be more reliable than any one of the measurements considered separately. In Chapter 5 we will prove that this is so; the uncertainty in the final answer X best = X bar turns out to be the SD, sigma x, DIVIDED BY SQRT (N). This quantity is called the SD OF THE MEAN, and is denoted by sigma x bar.
eq. 4.14 : sigma x bar = sigma x / sqrt (N)

(Other common names for this are STANDARD ERROR and STANDARD ERROR OF THE MEAN) Thus ......

Proof referred to above on pp. 127-130

bc tired of copy typing.

Jack Uretsky wrote:

Hi Tim-
Does one of the references distinguish - I repeat - distinguish between "standard deviation" and "standard deviation of the mean" ?
If so, could you kindly tell me which one?
Regards,
Jack

On Tue, 10 Oct 2006, Folkerts, Timothy J wrote:




Can someone direct me to an authoritative work on statistics that distinguishes between "standard deviation" and "standard deviation of the mean" ?


How about NIST? They have a great online applied stats references.

Here is a general discussion of error analysis
http://www.itl.nist.gov/div898/handbook/mpc/section5/mpc5.htm

Here is a bit on confidence intervals for means, which mentions "standard error".
http://www.itl.nist.gov/div898/handbook/eda/section3/eda352.htm

Or read the glossary for a quick (although rather dense) definition for "standard error"
http://www.itl.nist.gov/div898/handbook/glossary.htm


Tim Folkerts