DJN,

Well, this should get some interesting discussion going...

As Atul said, the Central Limit Theorem states that regardless of the parent population shape (a square distribution, triangular, bi-model, etc,) as the sample size becomes large compared to the parent (usually taken at a minimum of 30 samples) the average of the means is centered at the average of the raw data and the the standard deviation of the samples is related to the standard deviation of the raw data by a formula. So for a subgroup size of 5 the sample standard deviation is equal to 0.45 the standard deviation of the parent. At subgroup size of 4 the standard deviation of the x-bars is equal to 0.50 the standard deviation of the parent. So.... the parent population does not have to be normally distributed yet the sample distribution will always be normally distributed. If you test for normality and the sample population is not normally distributed, there is something wrong with the data or the data collection method.

While I agree with Atul on the eyeball method, I always confirm that with a graphical or calculated test.