[Phys-L] Re: Average earlier or average later?

[Brian Whatcott <betwys1@SBCGLOBAL.NET>]

At 07:56 AM 9/9/2005, you wrote:

> Maybe the following simple example would be worth discussing--
>
> Say you measure a series of times but your calculation will use the square
> of the time.
>
> T(s)       T-squared
> 5                25
> 4.75         22.5265
> 4.75         22.5265
> 4.75         22.5265
> 4.75         22.5265
> 6                36
> average
> 5               25.208
> stdev
> .5              5.38
> % dev
> 10              21.3
>
> Is there a clear cut choice here for choosing the square of the average or
> the average of the squares?  My gut is the square of the average, but being
> without formal training in stats, I'm not sure.  If I recall what little
> stats I've had correctly, squaring the value of 5+/-10% yields 25+/-20%.
>
> Rick
>
> *********************************************************
> Richard W. Tarara


Let's check out Rick's concrete case:
var (sec)  = 5 sec  +-10% =  [5.5...4.5 secs]

var squared = [30.25 ... 20.25 secs sq]

That could I suppose be expressed as  [25 secs sq +21%...  25 secs sq - 19%]

To illustrate that mutiplying a scattered variable skews the resulting average?

But....I am not using statistical methods, but only arithmetic.

Brian Whatcott    Altus OK    Eureka!
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