Vincent Le Chevalier wrote:
> Darren New wrote:
>> Invisible wrote:
>>> Can anybody tell me what the value of some other statistics should 
>>> hypothetically be? (Geometric mean, harmonic mean, quadratic mean, 
>>> standard deviation...)
>>
>> I would think if you look up the definitions and then put in the set 
>> of numbers 1..k, you should come up with the answer, yes? Or is that 
>> not how statistics works?
> 
> I think he is looking for the value predicated based on the probability 
> distribution, not the estimated value for one particular set of data.

That's what I understood. If he has a linear set of data, wouldn't it 
theoretically be equal quantities of each value, and hence wouldn't the 
statistics work to calculate the value from just one set of numbers per k?

> Quadratic mean and standard deviation should be fairly easy to find, as 
> here:
> http://mathworld.wolfram.com/UniformDistribution.html
> Quadratic mean = sqrt(k^2/3)
> Standard deviation = sqrt(k^2/12)
> (Quite easy to compute with a simple integral, too).

Oh, you mean "closed form". Yes, I guess that might be a little harder to 
figure out without the math to close over the expression. (I'm kind of 
curious where that 1/12'th comes from.)

I often have (unimportant, idle) questions like "how many times can I expect 
to roll a die before I've seen every face" or "... before a 1 comes up" or 
some such. Never bothered to actually write it down somewhere once I looked 
it up, tho. I suspect if I had to figure it out myself, I'd remember it.

-- 
Darren New, San Diego CA, USA (PST)
   Forget "focus follows mouse." When do
   I get "focus follows gaze"?

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