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

["Pamela L. Gay" <pgay@FAS.HARVARD.EDU>]

Okay I'm game for a simulation. Played with excel for 30 seconds and for
     N = 1000
     <X_N> = 2.200
     stdev(X_N) = 0.374

I found
     Y=  Sum over N (X_N)^4  / N = 27.499
     Y = <X_N>^4 = 23.423

Cheers,
Pamela


On Sep 9, 2005, at 11:23 AM, ludwik kowalski wrote:
> A numerical illustration:
> 1) Y=T^4 (measuring temperature to calculate the rate of cooling by
> radiation, Y)
> 2) Three values of T' were measured: 1, 2 and 3. The mean T' is 2 and
> we conclude that the true Y is close to 16.
> 3) Without calculating mean T' we calculate individual Y' from
> individual T' as: 1, 16 and 81. And we conclude that the true Y is
> close 36.
>
> It is the propagation of error issue. We know that Y=T^4 is highly
> reliable. And our object is definitely loosing heat by radiation at
> some unknown rate, Y. We measured T three times and made two
> conclusions based on different methods. My desktop computer is
> dead. If
> it were not dead I would simulate the situation by randomizing T with
> True Basic. That would definitely tell me which of the two methods is
> better. That is what computer simulations are good for.
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