The comments about mean=median=mode, skewness = 0, kurtosis =3, are very unlikely to hold for real data. The normal distribution is an idealized model that describes general characteristics very well, but rarely (i would argue never) is exactly correct.
The tests typically allow you to conclude that your data "isn't significantly different" than what you expect from the normal model. Histograms are decidedly poor as an aid, since too much depends on the choices for bin width (and so number of bins) and the sample size.
You might look at the Kolmogorov-Smirnoff test (http://mathworld.wolfram.com/Kolmogo...irnovTest.html
which compares your sample's empirical distribution to a normal distribution, although it works best when you don't estimate the mean and standard deviation with the sample values.
q-q plots (quantile-quantile plots) are a useful visual tool.
what often occurs is you will see your data set resembling a normal distribution "in the middle", but problems will occur in the extremes (tails) - sadly, that's often the region in which you have the most interest.
Good luck with your investigations.