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Re: Question - deviation of elements in a population

  • To: mathgroup at smc.vnet.net
  • Subject: [mg124611] Re: Question - deviation of elements in a population
  • From: Bill Rowe <readnews at sbcglobal.net>
  • Date: Thu, 26 Jan 2012 03:30:16 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

On 1/25/12 at 7:03 AM, kallen.hair at gmail.com (Kallen Hair) wrote:

>This is a simple question but I need to get it right. I have a
>population of 4 values and need to find out if they are all with in
>a certian percentage tolerance of each other.

>For example I have 4 values [21 20 22 19] and a tolerance of 10%.

>Would this be as easy as (1 - min/max) > tolerance, (1-19/22) > 0.1
>=> 0.136 > 0.1 therefore the population is not within 10% of each
>other.

>Or would I calculate the mean, find out the max deviation from the
>mean based on the tolerance and check if each value is in or outside
>this tolerance? For the same values as above this would be; Mean =
>20.5 therefore a tolerance of 20.5 * 0.1 = 2.05. This means all
>values minus the mean are within +- the calculated tolerance and the
>population is valid.

>Which one is more valid?

Both methods are equally valid. Which method you use will depend
on details of your application.

For example, suppose these values were resistance values that I
might use in a circuit to control timing. In this application,
my ideal value might be say 20 ohms and I could live with
anything within 10% of 20 ohms. If the resistors were selected
from a group with a mean of 20 ohms, the best procedure would be
to compute the mean of the resistors then the deviation from the
mean in per cent.

But change the application. Suppose I wanted to use two of these
to form a resistor divider. Now I would be concerned about the
percent deviation of one part relative to another part and would
not want the percent deviation from the mean value.




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