Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started 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?

I don't see what the problem is here.

There is a difference here (95+95)/2 = 95 while (95*95)^0.5 = + or  95

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 . . . .

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
(1100900)=200,, then 200/2=100,,
after 1100100=1000Hz or 900+100=1000Hz
Which one should I use [???]
and Why

You have 3 options.
(A+B)/2
Root (AB)
A+ (0.5*(AB))
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.

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 f_{0} 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.. . . .

thanks. :)