

> Original Message
> From: [hidden email] [mailto: [hidden email]] On Behalf
> Of Ron Michael
> Sent: Wednesday, January 16, 2008 12:15 AM
> To: [hidden email]
> Subject: [R] Different results in calculating SD of 2 numbers
>
> Hi all,
>
> Can anyone tell me why I am getting different results in calculating SD of 2 numbers ?
>
> > (1.250.95)/2
> [1] 0.15
Because the above is not the standard deviation of two numbers. The sample based estimate of the population standard deviation of a set of numbers (which is what sd() computes) is
(sum((xmean(x))^2 )/(length(x)1))^.5
which for your two numbers would be
( (1.25  1.1)^2 + (.95  1.1)^2 )^.5
> > sd(c(1.25, 0.95))
> [1] 0.2121320 # why it is different from 0.15?
>
> Regards,
>
Hope this is helpful,
Dan
Daniel Nordlund
Bothell, WA USA
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>>>>> "RM" == Ron Michael < [hidden email]>
>>>>> on Wed, 16 Jan 2008 00:14:56 0800 (PST) writes:
RM> Hi all,
RM> Can anyone tell me why I am getting different results in calculating SD of 2 numbers ?
>> (1.250.95)/2
RM> [1] 0.15
>> sd(c(1.25, 0.95))
RM> [1] 0.2121320 # why it is different from 0.15?
because 1 is different from 2 !
If 2 was 1, than sqrt(2) == 1 as well, but actually I don't
think the universe and we all would exist in that case ....
Martin Maechler, ETH
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On 16Jan08 08:45:04, Martin Maechler wrote:
>>>>>> "RM" == Ron Michael < [hidden email]>
>>>>>> on Wed, 16 Jan 2008 00:14:56 0800 (PST) writes:
>
> RM> Hi all,
> RM> Can anyone tell me why I am getting different results in
> calculating SD of 2 numbers ?
>
> >> (1.250.95)/2
> RM> [1] 0.15
> >> sd(c(1.25, 0.95))
> RM> [1] 0.2121320 # why it is different from 0.15?
>
> because 1 is different from 2 !
> If 2 was 1, than sqrt(2) == 1 as well, but actually I don't
> think the universe and we all would exist in that case ....
> Martin Maechler, ETH
Of course we would!!  Since FALSE implies X is TRUE for any X.
But FALSE would also imply that X is FALSE, so you are entitled
to your view as well, Martin.
With best wishes,
Ted.

EMail: (Ted Harding) < [hidden email]>
Faxtoemail: +44 (0)870 094 0861
Date: 16Jan08 Time: 09:47:20
 XFMail 
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(Ted Harding) wrote:
> On 16Jan08 08:45:04, Martin Maechler wrote:
>
>>>>>>>"RM" == Ron Michael < [hidden email]>
>>>>>>> on Wed, 16 Jan 2008 00:14:56 0800 (PST) writes:
>>
>> RM> Hi all,
>> RM> Can anyone tell me why I am getting different results in
>>calculating SD of 2 numbers ?
>>
>> >> (1.250.95)/2
>> RM> [1] 0.15
>> >> sd(c(1.25, 0.95))
>> RM> [1] 0.2121320 # why it is different from 0.15?
>>
>>because 1 is different from 2 !
>>If 2 was 1, than sqrt(2) == 1 as well, but actually I don't
>>think the universe and we all would exist in that case ....
>>Martin Maechler, ETH
>
>
> Of course we would!!  Since FALSE implies X is TRUE for any X.
>
> But FALSE would also imply that X is FALSE, so you are entitled
> to your view as well, Martin.
>
Then again, as pi might have been equal to 1 prior to the Big Bang, I
see no reason why sqrt(2) shouldn't have been equal to 1 as well. After
all, in those days we were all one...
Jim
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At 11:32 16.01.2008, Jim Lemon wrote:
>(Ted Harding) wrote:
> > On 16Jan08 08:45:04, Martin Maechler wrote:
> >
> >>>>>>>"RM" == Ron Michael < [hidden email]>
> >>>>>>> on Wed, 16 Jan 2008 00:14:56 0800 (PST) writes:
> >>
> >> RM> Hi all,
> >> RM> Can anyone tell me why I am getting different results in
> >>calculating SD of 2 numbers ?
> >>
> >> >> (1.250.95)/2
> >> RM> [1] 0.15
> >> >> sd(c(1.25, 0.95))
> >> RM> [1] 0.2121320 # why it is different from 0.15?
> >>
> >>because 1 is different from 2 !
> >>If 2 was 1, than sqrt(2) == 1 as well, but actually I don't
> >>think the universe and we all would exist in that case ....
> >>Martin Maechler, ETH
> >
> >
> > Of course we would!!  Since FALSE implies X is TRUE for any X.
> >
> > But FALSE would also imply that X is FALSE, so you are entitled
> > to your view as well, Martin.
> >
>Then again, as pi might have been equal to 1 prior to the Big Bang, I
>see no reason why sqrt(2) shouldn't have been equal to 1 as well. After
>all, in those days we were all one...
>
>Jim
>
Of course the question is off topic, but I like it. In my
understanding mathematics is a theoretical model, that may or may not
describe properly certain aspects of a "reality". I cannot see, why a
theoretical model should have any influence on our existence, as long
as we don't apply it in an unreasonable way.
To believe in our existence or to prove it is a totally different case.
Heinz
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And another problem, in addition to the points made by others, is that
the formula for the SD gives a biased estimate (it underestimates it) of
the population SD for small n when sampling from a normal distribution.
When n is about twelve or so or more, the bias can usually be ignored
(it is about 2.2%), but when you have only two numbers, the correction
factor is about 1.25.
The approximate correction formula, as I understand it, is
(n.75)/(n1), so if n = 2, then it is 1.25/1, but this is not exact.
The "real" formula is more complex (not difficult, but involves the
gamma function) and my reference to it is not at this office, or I would
give it.
HTH,
Ben
Original Message
From: [hidden email] [mailto: [hidden email]]
On Behalf Of Ron Michael
Sent: Wednesday, January 16, 2008 2:15 AM
To: [hidden email]
Subject: [PS] [R] Different results in calculating SD of 2 numbers
Hi all,
Can anyone tell me why I am getting different results in calculating SD
of 2 numbers ?
> (1.250.95)/2
[1] 0.15
> sd(c(1.25, 0.95))
[1] 0.2121320 # why it is different from 0.15?
Regards,
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http://uk.messenger.yahoo.com
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