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Question - deviation of elements in a population

• To: mathgroup at smc.vnet.net
• Subject: [mg124569] Question - deviation of elements in a population
• From: Kallen Hair <kallen.hair at gmail.com>
• Date: Wed, 25 Jan 2012 07:03:11 -0500 (EST)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

Hello,

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? I could also use the standard deviation but
im not sure how to relate this to a percentage. Any help would be
appretiated thankyou.