Naked Science Forum

Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: erickejah on 24/06/2009 23:38:16

Title: What is the difference between this two calculations?
Post by: erickejah on 24/06/2009 23:38:16
(95+95)/2 and √(95*95)

mod:
when do I have to use each and what is the specific purpose of each one?
Title: What is the difference between this two calculations?
Post by: Chemistry4me on 25/06/2009 06:08:33
I don't see what the problem is here.
Title: What is the difference between this two calculations?
Post by: syhprum on 25/06/2009 07:27:46
There is a difference here (95+95)/2 = 95 while (95*95)^0.5 = + or - 95
Title: What is the difference between this two calculations?
Post by: lyner on 25/06/2009 09:27:37
You have shown formulae for the arithmetic mean and geometric mean of two numbers.
The answers are only the  same (magnitude) when the two numbers happen to be both the same.
When is one formula more appropriate than the other? It all depends . . . .
Title: What is the difference between this two calculations?
Post by: erickejah on 26/06/2009 00:08:05
arithmetic mean and geometric mean of two numbers.
It all depends . . . .
For example:
there is a bandwidth of 200Hz for a band pass filter. The central critical frequency is 1000Hz.

we can assume that the lower limit is 900hz and the upper limit is 1100Hz.

okay, what if I'm only given the upper and lower limits?
upper limit=1100 and  lower limit=900
How should I calculate the central critical frequency?
→By using the arithmetic mean I obtain:
 (1100+900)/2=1000Hz
→By using the geometric mean I obtain:
 (1100*900)^0.5=994.99Hz
→or
 (1100-900)=200,, then 200/2=100,,
 after 1100-100=1000Hz or 900+100=1000Hz

Which one should I use   [???]
 and Why
Title: What is the difference between this two calculations?
Post by: Bored chemist on 26/06/2009 06:58:44
You have 3 options.
(A+B)/2
Root (AB)
A+ (0.5*(A-B))
The first and last give the same answer (and always will for A>B) the second gives a different, incorrect, answer. (Assuming that 1000 is the right answer)
Use the first one because it's easiest to calculate.

Howeve, I'm pretty sure it's possible to make a filter with an unsymmetrical response.
Title: What is the difference between this two calculations?
Post by: lyner on 27/06/2009 16:31:43
I think the arithmetic mean would often be more appropriate in that sort of problem (where there's some modulation involved) because sidebands occur symmetrically about the carrier frequency. A symmetrical filter, centred about f0 is what is normally called for.

Of course, when calculating average speeds, and the like, it is often appropriate to use the Harmonic Mean
= 1/2(1/x+1/y)

And the median and mode may be even more appropriate etc. etc.. . . .
Title: What is the difference between this two calculations?
Post by: erickejah on 28/06/2009 02:49:38
thanks. :)