Missing quartile in boxplot Currently I am creating a box plot. I am new on the field of statistics and especially box plots. Find the picture following: 
On the y-axis find the number of messages. I have problems understanding what I see there. The plot is created by Matlab automatically. As I know there should be four quartile in a box plot. I see there only three. Probably this happened because of the value of the median (it is the green line). But I do not know what this means if a quartile is missing. Is somebody around here who can may be explain this and tell me some details, what you can read out of the plot?
 A: The "box" in a boxplot extends from the first to the third quartile, i.e., from the 25th to the 75th percentile. Visually, this means that your 25th percentile is around 6 messages, and your 75th percentile around 8.
In addition, boxplots indicate the median (i.e., the second quartile, or 50th percentile) using a horizontal line.
Of course, the median can coincide with a quartile. Good implementations therefore use a different color or line type for the median line. In the present case, we see that the bottom horizontal line is green. It is obviously plotted over the first quartile line. Thus, this is not only the first quartile, but simultaneously the median. Therefore, your median is also about 6.
You should be able to verify this from your data, by calculating the quartiles and the median.
A: The median is probably identical to the first quartile, which is why they overlap. This tends to happen when you have a large proportion of identical, low values in the dataset. Here's an example that reproduces this pattern: 
dat <- c(1,2,2,2,3,5,6)

median(dat)
## 2
quantile(dat, 0.25)
## 25% 
##  2 

boxplot(dat)


You can read a basic introduction about how to interpret boxplots here. Though as Nick Cox points out below, its discussion of what are called 'outliers' is flawed and should be ignored. Outliers should not be deleted unless there is very strong reason to, such as a clear data recording error. 
Note also that a boxplot is not a great way to display many datasets. I agree with Stephan Kolassa's recommendation of a beeswarm plot for small datasets and a violin plot/kernel density plot for larger ones. 
