# [R] [PS] Different results in calculating SD of 2 numbers

Ben Fairbank BEN at SSANET.COM
Wed Jan 16 18:08:13 CET 2008

```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

The approximate correction formula, as I understand it, is
(n-.75)/(n-1), 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: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
On Behalf Of Ron Michael
Sent: Wednesday, January 16, 2008 2:15 AM
To: r-help at stat.math.ethz.ch
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 ?

> (1.25-0.95)/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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