# How to determine an appropriate sample size for a normal distributed population?

I am trying to extract a sample from a given population. Assuming the population distribution is normal (I still have to test it, but I am confident it is), since the number of observations in the population is too high to perform some tests I need to do with my laptop (N>50,000), I'd like to extract a smaller sample from it.

My questions are:

1. What would be a good sampling method to avoid including values lying inthe tails of the population into the extracted sample and
2. what would be the best sample size?

As far as I know, I thought random sampling won't let me achieve what I want in question 1, as the probability of picking up an outlier rather than a value closer to the mean is the same (although the number of my outliers is very low). Am I wrong?

Secondly, I know the estimation of the sample size depends on the error I want to allow. So, in the light of these few things I know, I am asking if someone could help me getting me a bit further into this, and hopefully providing some useful an to-the-point reference.

Thanks in advance to those who might want to help me clarifying this.

• I am amazed you could apply a Shapiro-Wilk test to a dataset of 50,000 observations that contains outliers and have it conclude the distribution is normal. That just does not seem possible.
– whuber
Feb 12, 2015 at 18:05
• indeed the function (ran on MATLAB) tells me there are too many observations (the maximum available is 5000), but still gives me an output. Nevertheless, I might say the distribution of my population is normal by some tests performed on various subsets of it. So, the assunption is that it is normal distributed. Feb 12, 2015 at 22:04
• Then please tell us what an "outlier" could possibly be. I cannot see how a population can at one and the same time be so perfectly normal and have outliers.
– whuber
Feb 12, 2015 at 22:06
• "I know the population distribution is normal" -- no, you don't know that. Feb 13, 2015 at 7:37
• I would recommend you abandon this effort to formulate your question abstractly. It sounds like you want to learn something from an image. So, tell us about your image (what does it represent? how was it created? what are its basic statistical characteristics?) and what you would like to learn (such as the "tests" you refer to). Ask about appropriate ways to accomplish that. This will at once make your question understandable, narrow it enough to make it answerable, and open up the possibility of creative answers that could be far more useful than the approach you are currently thinking of.
– whuber
Feb 13, 2015 at 16:38