Do the data come from a normal distribution?
A histogram of the data can be examined and may indicate that there is skewness or that the distribution separates into clusters. However if the data set is large, a normal probability plot can indicate more subtle departures from a normal distribution.
Examples
How much curvature is needed to suggest non-normality?
In the examples above, linearity or nonlinearity in the probability plot was clear. In practice however, the randomness of real data means that the probability plot will not be exactly straight even when the data are sampled from a normal population.
How much curvature is needed to conclude that the underlying distribution is not normal?
This is a difficult question to answer and we will not address it here.