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I have 100,000 customers, each customer has a few variables associated with them, separated into 100 groups. I want to find a sample of 10 groups that best represents the entire 100 groups. What are my best options for doing this?

Should I just look at overall mean and st. dev for the variables and find the 10 groups that have the closest match?

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    $\begingroup$ What do you need this for? Look at the aspects which are important for you, and then define similarity using them. $\endgroup$ – kjetil b halvorsen Dec 10 '15 at 19:11
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Technically, simple random sampling from the population will produce a sample that is representative. That just means picking each individual with equal probability.

Alternately if you know some basic demographic information about the sample, you can draw a stratified sample which is not representative. However, stratified samples can be weighted to produce more efficient estimates of population attributes than in the simple-random samples.

What you are describing: selecting individuals whose characteristics are close to the population mean will not produce a representative sample and will probably bias all your results in a way that weighting cannot easily address. As an example, if you divide your customers according to volume/frequency to inspect the things they buy, the mode purchasing pattern will probably be high frequency / low volume customers. These customers, however, may not be the major revenue contributor for your company. You are omitting the purchases of low frequency / high volume purchasers whose demands may actually be different, whose desired products are different, and whose cost preferences determine whether they move their entire batch purchases to another vendor or stay with you.

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    $\begingroup$ (+1) very good point emphasizing common misconception about "representative" sampling! Maybe you could provide a short example or description of why selecting "average" individuals would lead to biased sample -- it would make your answer even more valuable. $\endgroup$ – Tim Dec 10 '15 at 20:32

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