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.