Histogram, box plot and probability plot - which is better for assessing normality? Which method of the three: histogram, box plot and probability plot is best at determining whether a distribution is approximately normally distributed? Why?
 A: Normal probability plots: The main purpose of a normal probability plot (normal Q-Q plot) is to assess normality. Here are
plots, each of $n = 500$ observations, from uniform, normal, and Laplace (double-exponential) families, respectively. Only the normal sample shows points along
a reasonably straight line in its normal probability plot. Of the three
kinds of graphs a normal probability plot is most directly relevant to
assessing normality.

Boxplots: Major purposes of boxplots are to show quartiles--and also outliers, if
any are present. The boxplots below are for the same three datasets as
above. All three distributions are symmetrical, and their respective
boxplots are almost symmetrical. First and third quartiles (ends of boxes)
become closer together as we scan from left to right.
In a boxplot, outliers are plotted individually as dots. A uniform distribution has no 'tails',
and outliers are rare. A normal distribution has long thin tails, and
and a boxplot of a moderately large sample will typically show a few
outliers (in each tail). A Laplace distribution has heavy tails, and it is rare for
a boxplot not to show many outliers. 
If a boxplot shows many far outliers or if the whiskers are greatly
different in length, then the population from which the sample came
is unlikely to be normal. However, boxplots may be the weakest of
the three kinds of plots in assessing normality. (They are better at
showing a sample is not normal, than confirming that it is.)

Histograms: Below we show histograms of the three samples along
with the respective density functions of their populations.
Especially for small samples, important information can be lost
when data are sorted into histogram bins. Even with our moderately large
samples, the 
shape of the histogram is not necessarily a close match with
the shape of the population distribution. Nevertheless, of the three
kinds of graphical descriptions, histograms may be second-best (to
normal probability plots) for assessing normality.

A: *

*Generally the boxplot is by far the least informative; it gives only a few pieces of information about the whole sample.
This leads to dangers of them being quite misleading about what you have. 
Compare these four histograms and the corresponding boxplots:

(how to create these samples is given here: Box-and-whisker plot for multimodal distribution)
As we see there, very different-looking histograms (which in this case are mostly showing you what's going on, though they do obscure some particular features) correspond to identical boxplots.

*The histogram can be more informative but typical default settings use far too few bins. 
Histograms have their own dangers, but they're rarer. These two histograms are of the same data:

The data for this example is given at: Assessing approximate distribution of data based on a histogram

*Probability plots / quantile-quantile plots are usually the most informative - they show "all the data" - but are harder to learn to read.
There's some guidance on reading them here How to interpret a Q-Q plot
